Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 3110 and 3114 the smallest integer that is 4842270 that is divisible by both numbers.
Least Common Multiple (LCM) of 3110 and 3114 is 4842270.
LCM(3110,3114) = 4842270
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 3110 and 3114. First we will calculate the prime factors of 3110 and 3114.
Prime Factorization of 3110
2 | 3110 |
5 | 1555 |
311 | 311 |
1 |
Prime factors of 3110 are 2, 5,311. Prime factorization of 3110 in exponential form is:
3110 = 21×51×3111
Prime Factorization of 3114
2 | 3114 |
3 | 1557 |
3 | 519 |
173 | 173 |
1 |
Prime factors of 3114 are 2, 3,173. Prime factorization of 3114 in exponential form is:
3114 = 21×32×1731
Now multiplying the highest exponent prime factors to calculate the LCM of 3110 and 3114.
LCM(3110,3114) = 21×32×51×1731×3111
LCM(3110,3114) = 4842270
Factors of 3110
List of positive integer factors of 3110 that divides 3110 without a remainder.
1, 2, 5, 10, 311, 622, 1555, 3110
Factors of 3114
List of positive integer factors of 3114 that divides 3114 without a remainder.
1, 2, 3, 6, 9, 18, 173, 346, 519, 1038, 1557, 3114
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3110 and 3114, than apply into the LCM equation.
GCF(3110,3114) = 2
LCM(3110,3114) = ( 3110 × 3114) / 2
LCM(3110,3114) = 9684540 / 2
LCM(3110,3114) = 4842270
(i) The LCM of 3114 and 3110 is associative
LCM of 3110 and 3114 = LCM of 3114 and 3110
1. What is the LCM of 3110 and 3114?
Answer: LCM of 3110 and 3114 is 4842270.
2. What are the Factors of 3110?
Answer: Factors of 3110 are 1, 2, 5, 10, 311, 622, 1555, 3110. There are 8 integers that are factors of 3110. The greatest factor of 3110 is 3110.
3. What are the Factors of 3114?
Answer: Factors of 3114 are 1, 2, 3, 6, 9, 18, 173, 346, 519, 1038, 1557, 3114. There are 12 integers that are factors of 3114. The greatest factor of 3114 is 3114.
4. How to Find the LCM of 3110 and 3114?
Answer:
Least Common Multiple of 3110 and 3114 = 4842270
Step 1: Find the prime factorization of 3110
3110 = 2 x 5 x 311
Step 2: Find the prime factorization of 3114
3114 = 2 x 3 x 3 x 173
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4842270 = 2 x 3 x 3 x 5 x 173 x 311
Step 4: Therefore, the least common multiple of 3110 and 3114 is 4842270.