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Least Common Multiple of 40 and 52

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 40 and 52 is 520.

LCM(40,52) = 520

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Least Common Multiple of 40 and 52 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40 and 52, than apply into the LCM equation.

GCF(40,52) = 4
LCM(40,52) = ( 40 × 52) / 4
LCM(40,52) = 2080 / 4
LCM(40,52) = 520

Least Common Multiple (LCM) of 40 and 52 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 40 and 52. First we will calculate the prime factors of 40 and 52.

Prime Factorization of 40

Prime factors of 40 are 2, 5. Prime factorization of 40 in exponential form is:

40 = 23 × 51

Prime Factorization of 52

Prime factors of 52 are 2, 13. Prime factorization of 52 in exponential form is:

52 = 22 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 40 and 52.

LCM(40,52) = 23 × 51 × 131
LCM(40,52) = 520

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