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What is the Least Common Multiple of 27354 and 27370?

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 27354 and 27370 is 374339490.

LCM(27354,27370) = 374339490

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Least Common Multiple of 27354 and 27370 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27354 and 27370, than apply into the LCM equation.

GCF(27354,27370) = 2
LCM(27354,27370) = ( 27354 × 27370) / 2
LCM(27354,27370) = 748678980 / 2
LCM(27354,27370) = 374339490

Least Common Multiple (LCM) of 27354 and 27370 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27354 and 27370. First we will calculate the prime factors of 27354 and 27370.

Prime Factorization of 27354

Prime factors of 27354 are 2, 3, 47, 97. Prime factorization of 27354 in exponential form is:

27354 = 21 × 31 × 471 × 971

Prime Factorization of 27370

Prime factors of 27370 are 2, 5, 7, 17, 23. Prime factorization of 27370 in exponential form is:

27370 = 21 × 51 × 71 × 171 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 27354 and 27370.

LCM(27354,27370) = 21 × 31 × 471 × 971 × 51 × 71 × 171 × 231
LCM(27354,27370) = 374339490