Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 3100 and 3102 the smallest integer that is 4808100 that is divisible by both numbers.
Least Common Multiple (LCM) of 3100 and 3102 is 4808100.
LCM(3100,3102) = 4808100
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 3100 and 3102. First we will calculate the prime factors of 3100 and 3102.
Prime Factorization of 3100
2 | 3100 |
2 | 1550 |
5 | 775 |
5 | 155 |
31 | 31 |
1 |
Prime factors of 3100 are 2, 5,31. Prime factorization of 3100 in exponential form is:
3100 = 22×52×311
Prime Factorization of 3102
2 | 3102 |
3 | 1551 |
11 | 517 |
47 | 47 |
1 |
Prime factors of 3102 are 2, 3, 11,47. Prime factorization of 3102 in exponential form is:
3102 = 21×31×111×471
Now multiplying the highest exponent prime factors to calculate the LCM of 3100 and 3102.
LCM(3100,3102) = 22×31×52×111×311×471
LCM(3100,3102) = 4808100
Factors of 3100
List of positive integer factors of 3100 that divides 3100 without a remainder.
1, 2, 4, 5, 10, 20, 25, 31, 50, 62, 100, 124, 155, 310, 620, 775, 1550, 3100
Factors of 3102
List of positive integer factors of 3102 that divides 3102 without a remainder.
1, 2, 3, 6, 11, 22, 33, 47, 66, 94, 141, 282, 517, 1034, 1551, 3102
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3100 and 3102, than apply into the LCM equation.
GCF(3100,3102) = 2
LCM(3100,3102) = ( 3100 × 3102) / 2
LCM(3100,3102) = 9616200 / 2
LCM(3100,3102) = 4808100
(i) The LCM of 3102 and 3100 is associative
LCM of 3100 and 3102 = LCM of 3102 and 3100
1. What is the LCM of 3100 and 3102?
Answer: LCM of 3100 and 3102 is 4808100.
2. What are the Factors of 3100?
Answer: Factors of 3100 are 1, 2, 4, 5, 10, 20, 25, 31, 50, 62, 100, 124, 155, 310, 620, 775, 1550, 3100. There are 18 integers that are factors of 3100. The greatest factor of 3100 is 3100.
3. What are the Factors of 3102?
Answer: Factors of 3102 are 1, 2, 3, 6, 11, 22, 33, 47, 66, 94, 141, 282, 517, 1034, 1551, 3102. There are 16 integers that are factors of 3102. The greatest factor of 3102 is 3102.
4. How to Find the LCM of 3100 and 3102?
Answer:
Least Common Multiple of 3100 and 3102 = 4808100
Step 1: Find the prime factorization of 3100
3100 = 2 x 2 x 5 x 5 x 31
Step 2: Find the prime factorization of 3102
3102 = 2 x 3 x 11 x 47
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4808100 = 2 x 2 x 3 x 5 x 5 x 11 x 31 x 47
Step 4: Therefore, the least common multiple of 3100 and 3102 is 4808100.