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What is the Least Common Multiple of 36974 and 36992?

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 36974 and 36992 is 683871104.

LCM(36974,36992) = 683871104

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Least Common Multiple of 36974 and 36992 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 36974 and 36992, than apply into the LCM equation.

GCF(36974,36992) = 2
LCM(36974,36992) = ( 36974 × 36992) / 2
LCM(36974,36992) = 1367742208 / 2
LCM(36974,36992) = 683871104

Least Common Multiple (LCM) of 36974 and 36992 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 36974 and 36992. First we will calculate the prime factors of 36974 and 36992.

Prime Factorization of 36974

Prime factors of 36974 are 2, 7, 19, 139. Prime factorization of 36974 in exponential form is:

36974 = 21 × 71 × 191 × 1391

Prime Factorization of 36992

Prime factors of 36992 are 2, 17. Prime factorization of 36992 in exponential form is:

36992 = 27 × 172

Now multiplying the highest exponent prime factors to calculate the LCM of 36974 and 36992.

LCM(36974,36992) = 27 × 71 × 191 × 1391 × 172
LCM(36974,36992) = 683871104