Christ's atonement is sufficient for salvation that is for sure.  
 
I feel though ( and if I am wrong please accept my apologies) that your real question is does saying you BELIEVE in Christ sufficient for his atonement to cover your sins? 
 
The answer to that question is unequivocally NO! Christ himself told us that believe in his name alone is not sufficient for salvation. Christ proclaims in both Matthew and Luke that simply calling upon the name of the Lord or saying that you are doing works in his name is not enough, he will still denying knowing many whom claim to work in His name because there work was not for him but for personal gratification or gain.  
 
So the name of Christ or saying I am doing this in the name of the Lord is not enough, you can do that your entire life but if your heart is not focused on Christ those words are useless and only stand to condemn you on the day of judgement when your true motives are revealed.  
 
Christ tells us the conditions of salvation in the Gospels repeat this message again and again, whenever Christ heals or forgives sin he mentions faith.  
 
Faith is to have a contrite heart and a humble spirit to regret and feel ashamed for our sins and to repent of them and forsake them.  
 
Faith is also action though "For as the body without the spirit is dead, so faith without works is dead also" (James 2:26) So we are encouraged and commanded by the Lord to "take up (our) cross daily and follow me" (Luke 9:23).  
 
So salvation comes from faith in Christ and to have faith you must have works to show it by since faith without works is dead faith. It is hard to follow Christ daily without doing constant service to your fellow man since that is the entire ministry of the Savior.  
 
This is why the traditional concept of belief in Christ is sufficient for salvation is wrong. Satan believes in Christ, he believes with all his heart, mind, and soul, yet he can never receive salvation because his works, hie rebellion is unforgivable.  
 
Salvation is not just about pray but about moving from that prayer and doing good in the world for the glory of Heavenly Father and taking no credit at all for the fruits of that labor.  
 
Through works we have, grow, and show our faith in Christ (though the works them selves are useless on there own without faith) and through that faith we are saved by the atonement of the Lord Jesus Christ. There is no other way to salvation than this.  
 
This can be quite confusing so I apologize if that is what happens as you read. The important thing to know is that some accuse the LDS Church of believing that our works save us not the atonement of Jesus Christ, that we are trying to work our way into salvation. This concept is false, we believe that faith cannot exist without works, and that one cannot be saved without faith.  
 
We bear our fruits of service to make us better Christians and give glory to Christ and Heavenly Father. They do not give us salvation, but they show the Lord by serving our fellow man in His stead how much we love his and thank him for his atonement that we are unworthy to have but he freely and mercifully gives to all!

Eternal life means two different things to latter-day saints.  
 
The first definition is everlasting life. This is given freely to all mankind because of the atonement.  
 
The second definition is the quality of life that God lives (related scripture that comes to mind: 1 Cor. 15:40); to be joint heirs with Christ. This is available to all people who have lived on this earth who strive to be obedient to Gods laws and ordinances. 
 
To receive the gift of eternal life one must exercise faith in Jesus Christ (John 3:36), repent (Acts 17:30), be baptized in His name for the remission of ones sins (John 3:5), and receive the Holy Ghost. The believer must than strive to keep the commandments and to do the work of righteousness; primarily charity (1 Cor. 13). One must also endure to the end (Rom. 2:7). 
 
What this means is that someone who has lived a righteous life, and has done their best to follow the commandments, and to follow truth as they have found it will receive eternal life.  
 
If someone has never received a witness of the Holy Ghost that the LDS church is true and they never join, they are just as eligible for this as anyone else according to their works and faith. Those on the other side of the spectrum may be held more accountable if they received a witness from the Holy Ghost and never followed through with it.  
 
Only Christ can be the judge of this. We cannot determine another's worthiness to receive this gift regardless of circumstance. We know this for ourselves better than others. 
 
The purpose of the temple is to provide the ordinances that are required for these things to those who did not receive them (and also for ourselves the first time). Thus all mankind can be judged according to their faith and works by Christ.

So what you are saying is that belief is not enough; it has to be accompanied by works. Am I right? Are we then justified by our works or justified by faith in Christ alone? 
 
Thanks, Linda

This is correct. We believe that it requires both faith and works, works being the most important (1 Cor. 13).  
 
According to the New Testament (James 2: 14-18 KJV): 
 
What doth it profit, my brethren, though a man say he hath faith, and have not works? can faith save him? 
 
If a brother or sister be naked, and destitute of daily food, And one of you say unto them, Depart in peace, be ye warmed and filled; notwithstanding ye give them not those things which are needful to the body; what doth it profit? 
 
Even so faith, if it hath not works, is dead, being alone. 
 
Yea, a man may say, Thou hast faith, and I have works: shew me thy faith without thy works, and I will shew thee my faith by my works.