What is the Least Common Multiple of 2964 and 2976?
Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.
Least common multiple (LCM) of 2964 and 2976 is 735072.
LCM(2964,2976) = 735072
Least Common Multiple of 2964 and 2976 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2964 and 2976, than apply into the LCM equation.
GCF(2964,2976) = 12
LCM(2964,2976) = ( 2964 × 2976) / 12
LCM(2964,2976) = 8820864 / 12
LCM(2964,2976) = 735072
Least Common Multiple (LCM) of 2964 and 2976 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 2964 and 2976. First we will calculate the prime factors of 2964 and 2976.
Prime Factorization of 2964
Prime factors of 2964 are 2, 3, 13, 19. Prime factorization of 2964 in exponential form is:
2964 = 22 × 31 × 131 × 191
Prime Factorization of 2976
Prime factors of 2976 are 2, 3, 31. Prime factorization of 2976 in exponential form is:
2976 = 25 × 31 × 311
Now multiplying the highest exponent prime factors to calculate the LCM of 2964 and 2976.
LCM(2964,2976) = 25 × 31 × 131 × 191 × 311
LCM(2964,2976) = 735072
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