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What is the Least Common Multiple of 37740 and 37754?

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 37740 and 37754 is 712417980.

LCM(37740,37754) = 712417980

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Least Common Multiple of 37740 and 37754 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37740 and 37754, than apply into the LCM equation.

GCF(37740,37754) = 2
LCM(37740,37754) = ( 37740 × 37754) / 2
LCM(37740,37754) = 1424835960 / 2
LCM(37740,37754) = 712417980

Least Common Multiple (LCM) of 37740 and 37754 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37740 and 37754. First we will calculate the prime factors of 37740 and 37754.

Prime Factorization of 37740

Prime factors of 37740 are 2, 3, 5, 17, 37. Prime factorization of 37740 in exponential form is:

37740 = 22 × 31 × 51 × 171 × 371

Prime Factorization of 37754

Prime factors of 37754 are 2, 43, 439. Prime factorization of 37754 in exponential form is:

37754 = 21 × 431 × 4391

Now multiplying the highest exponent prime factors to calculate the LCM of 37740 and 37754.

LCM(37740,37754) = 22 × 31 × 51 × 171 × 371 × 431 × 4391
LCM(37740,37754) = 712417980