What is the Least Common Multiple of 72 and 86?
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 86 is 3096.
LCM(72,86) = 3096
Least Common Multiple of 72 and 86 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 86, than apply into the LCM equation.
GCF(72,86) = 2
LCM(72,86) = ( 72 × 86) / 2
LCM(72,86) = 6192 / 2
LCM(72,86) = 3096
Least Common Multiple (LCM) of 72 and 86 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 72 and 86. First we will calculate the prime factors of 72 and 86.
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 86
Prime factors of 86 are 2, 43. Prime factorization of 86 in exponential form is:
86 = 21 × 431
Now multiplying the highest exponent prime factors to calculate the LCM of 72 and 86.
LCM(72,86) = 23 × 32 × 431
LCM(72,86) = 3096