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What is the Least Common Multiple of 37004 and 37008?

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 37004 and 37008 is 342361008.

LCM(37004,37008) = 342361008

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Least Common Multiple of 37004 and 37008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37004 and 37008, than apply into the LCM equation.

GCF(37004,37008) = 4
LCM(37004,37008) = ( 37004 × 37008) / 4
LCM(37004,37008) = 1369444032 / 4
LCM(37004,37008) = 342361008

Least Common Multiple (LCM) of 37004 and 37008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37004 and 37008. First we will calculate the prime factors of 37004 and 37008.

Prime Factorization of 37004

Prime factors of 37004 are 2, 11, 29. Prime factorization of 37004 in exponential form is:

37004 = 22 × 111 × 292

Prime Factorization of 37008

Prime factors of 37008 are 2, 3, 257. Prime factorization of 37008 in exponential form is:

37008 = 24 × 32 × 2571

Now multiplying the highest exponent prime factors to calculate the LCM of 37004 and 37008.

LCM(37004,37008) = 24 × 111 × 292 × 32 × 2571
LCM(37004,37008) = 342361008