Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 3096 and 3100 the smallest integer that is 2399400 that is divisible by both numbers.
Least Common Multiple (LCM) of 3096 and 3100 is 2399400.
LCM(3096,3100) = 2399400
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 3096 and 3100. First we will calculate the prime factors of 3096 and 3100.
Prime Factorization of 3096
2 | 3096 |
2 | 1548 |
2 | 774 |
3 | 387 |
3 | 129 |
43 | 43 |
1 |
Prime factors of 3096 are 2, 3,43. Prime factorization of 3096 in exponential form is:
3096 = 23×32×431
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
Now multiplying the highest exponent prime factors to calculate the LCM of 3096 and 3100.
LCM(3096,3100) = 23×32×52×311×431
LCM(3096,3100) = 2399400
Factors of 3096
List of positive integer factors of 3096 that divides 3096 without a remainder.
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 43, 72, 86, 129, 172, 258, 344, 387, 516, 774, 1032, 1548, 3096
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
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3096 and 3100, than apply into the LCM equation.
GCF(3096,3100) = 4
LCM(3096,3100) = ( 3096 × 3100) / 4
LCM(3096,3100) = 9597600 / 4
LCM(3096,3100) = 2399400
(i) The LCM of 3100 and 3096 is associative
LCM of 3096 and 3100 = LCM of 3100 and 3096
1. What is the LCM of 3096 and 3100?
Answer: LCM of 3096 and 3100 is 2399400.
2. What are the Factors of 3096?
Answer: Factors of 3096 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 43, 72, 86, 129, 172, 258, 344, 387, 516, 774, 1032, 1548, 3096. There are 24 integers that are factors of 3096. The greatest factor of 3096 is 3096.
3. 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.
4. How to Find the LCM of 3096 and 3100?
Answer:
Least Common Multiple of 3096 and 3100 = 2399400
Step 1: Find the prime factorization of 3096
3096 = 2 x 2 x 2 x 3 x 3 x 43
Step 2: Find the prime factorization of 3100
3100 = 2 x 2 x 5 x 5 x 31
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 2399400 = 2 x 2 x 2 x 3 x 3 x 5 x 5 x 31 x 43
Step 4: Therefore, the least common multiple of 3096 and 3100 is 2399400.