What is the Least Common Multiple of 42 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 42 and 52 is 1092.
LCM(42,52) = 1092
Least Common Multiple of 42 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 42 and 52, than apply into the LCM equation.
GCF(42,52) = 2
LCM(42,52) = ( 42 × 52) / 2
LCM(42,52) = 2184 / 2
LCM(42,52) = 1092
Least Common Multiple (LCM) of 42 and 52 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 42 and 52. First we will calculate the prime factors of 42 and 52.
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 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 42 and 52.
LCM(42,52) = 22 × 31 × 71 × 131
LCM(42,52) = 1092