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What is the Least Common Multiple of 29976 and 29980?

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 29976 and 29980 is 224670120.

LCM(29976,29980) = 224670120

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Least Common Multiple of 29976 and 29980 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29976 and 29980, than apply into the LCM equation.

GCF(29976,29980) = 4
LCM(29976,29980) = ( 29976 × 29980) / 4
LCM(29976,29980) = 898680480 / 4
LCM(29976,29980) = 224670120

Least Common Multiple (LCM) of 29976 and 29980 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 29976 and 29980. First we will calculate the prime factors of 29976 and 29980.

Prime Factorization of 29976

Prime factors of 29976 are 2, 3, 1249. Prime factorization of 29976 in exponential form is:

29976 = 23 × 31 × 12491

Prime Factorization of 29980

Prime factors of 29980 are 2, 5, 1499. Prime factorization of 29980 in exponential form is:

29980 = 22 × 51 × 14991

Now multiplying the highest exponent prime factors to calculate the LCM of 29976 and 29980.

LCM(29976,29980) = 23 × 31 × 12491 × 51 × 14991
LCM(29976,29980) = 224670120