What is the Least Common Multiple of 42 and 53?
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 53 is 2226.
LCM(42,53) = 2226
Least Common Multiple of 42 and 53 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 53, than apply into the LCM equation.
GCF(42,53) = 1
LCM(42,53) = ( 42 × 53) / 1
LCM(42,53) = 2226 / 1
LCM(42,53) = 2226
Least Common Multiple (LCM) of 42 and 53 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 42 and 53. First we will calculate the prime factors of 42 and 53.
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 53
Prime factors of 53 are 53. Prime factorization of 53 in exponential form is:
53 = 531
Now multiplying the highest exponent prime factors to calculate the LCM of 42 and 53.
LCM(42,53) = 21 × 31 × 71 × 531
LCM(42,53) = 2226