What is the Least Common Multiple of 56 and 72?
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 56 and 72 is 504.
LCM(56,72) = 504
Least Common Multiple of 56 and 72 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 56 and 72, than apply into the LCM equation.
GCF(56,72) = 8
LCM(56,72) = ( 56 × 72) / 8
LCM(56,72) = 4032 / 8
LCM(56,72) = 504
Least Common Multiple (LCM) of 56 and 72 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 56 and 72. First we will calculate the prime factors of 56 and 72.
Prime Factorization of 56
Prime factors of 56 are 2, 7. Prime factorization of 56 in exponential form is:
56 = 23 × 71
Prime Factorization of 72
Prime factors of 72 are 2, 3. Prime factorization of 72 in exponential form is:
72 = 23 × 32
Now multiplying the highest exponent prime factors to calculate the LCM of 56 and 72.
LCM(56,72) = 23 × 71 × 32
LCM(56,72) = 504