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What is the Least Common Multiple of 31122 and 31135?

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 31122 and 31135 is 74537190.

LCM(31122,31135) = 74537190

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Least Common Multiple of 31122 and 31135 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31122 and 31135, than apply into the LCM equation.

GCF(31122,31135) = 13
LCM(31122,31135) = ( 31122 × 31135) / 13
LCM(31122,31135) = 968983470 / 13
LCM(31122,31135) = 74537190

Least Common Multiple (LCM) of 31122 and 31135 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31122 and 31135. First we will calculate the prime factors of 31122 and 31135.

Prime Factorization of 31122

Prime factors of 31122 are 2, 3, 7, 13, 19. Prime factorization of 31122 in exponential form is:

31122 = 21 × 32 × 71 × 131 × 191

Prime Factorization of 31135

Prime factors of 31135 are 5, 13, 479. Prime factorization of 31135 in exponential form is:

31135 = 51 × 131 × 4791

Now multiplying the highest exponent prime factors to calculate the LCM of 31122 and 31135.

LCM(31122,31135) = 21 × 32 × 71 × 131 × 191 × 51 × 4791
LCM(31122,31135) = 74537190