# What is the Least Common Multiple of 42 and 58?

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 58 is 1218.

LCM(42,58) = 1218

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## Least Common Multiple of 42 and 58 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 58, than apply into the LCM equation.

GCF(42,58) = 2
LCM(42,58) = ( 42 × 58) / 2
LCM(42,58) = 2436 / 2
LCM(42,58) = 1218

## Least Common Multiple (LCM) of 42 and 58 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 42 and 58. First we will calculate the prime factors of 42 and 58.

### 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 58

Prime factors of 58 are 2, 29. Prime factorization of 58 in exponential form is:

58 = 21 × 291

Now multiplying the highest exponent prime factors to calculate the LCM of 42 and 58.

LCM(42,58) = 21 × 31 × 71 × 291
LCM(42,58) = 1218