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What is the Least Common Multiple of 42 and 47?

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 42 and 47 is 1974.

LCM(42,47) = 1974

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Least Common Multiple of 42 and 47 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 42 and 47, than apply into the LCM equation.

GCF(42,47) = 1
LCM(42,47) = ( 42 × 47) / 1
LCM(42,47) = 1974 / 1
LCM(42,47) = 1974

Least Common Multiple (LCM) of 42 and 47 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42 and 47. First we will calculate the prime factors of 42 and 47.

Prime Factorization of 42

Prime factors of 42 are 2, 3, 7. Prime factorization of 42 in exponential form is:

42 = 21 × 31 × 71

Prime Factorization of 47

Prime factors of 47 are 47. Prime factorization of 47 in exponential form is:

47 = 471

Now multiplying the highest exponent prime factors to calculate the LCM of 42 and 47.

LCM(42,47) = 21 × 31 × 71 × 471
LCM(42,47) = 1974

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