What is the Least Common Multiple of 72 and 89?
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 72 and 89 is 6408.
LCM(72,89) = 6408
Least Common Multiple of 72 and 89 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72 and 89, than apply into the LCM equation.
GCF(72,89) = 1
LCM(72,89) = ( 72 × 89) / 1
LCM(72,89) = 6408 / 1
LCM(72,89) = 6408
Least Common Multiple (LCM) of 72 and 89 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 72 and 89. First we will calculate the prime factors of 72 and 89.
Prime Factorization of 72
Prime factors of 72 are 2, 3. Prime factorization of 72 in exponential form is:
72 = 23 × 32
Prime Factorization of 89
Prime factors of 89 are 89. Prime factorization of 89 in exponential form is:
89 = 891
Now multiplying the highest exponent prime factors to calculate the LCM of 72 and 89.
LCM(72,89) = 23 × 32 × 891
LCM(72,89) = 6408