What is the Least Common Multiple of 42 and 59?
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 59 is 2478.
LCM(42,59) = 2478
Least Common Multiple of 42 and 59 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 59, than apply into the LCM equation.
GCF(42,59) = 1
LCM(42,59) = ( 42 × 59) / 1
LCM(42,59) = 2478 / 1
LCM(42,59) = 2478
Least Common Multiple (LCM) of 42 and 59 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 42 and 59. First we will calculate the prime factors of 42 and 59.
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 59
Prime factors of 59 are 59. Prime factorization of 59 in exponential form is:
59 = 591
Now multiplying the highest exponent prime factors to calculate the LCM of 42 and 59.
LCM(42,59) = 21 × 31 × 71 × 591
LCM(42,59) = 2478