What is the Least Common Multiple of 65 and 84?
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 65 and 84 is 5460.
LCM(65,84) = 5460
Least Common Multiple of 65 and 84 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65 and 84, than apply into the LCM equation.
GCF(65,84) = 1
LCM(65,84) = ( 65 × 84) / 1
LCM(65,84) = 5460 / 1
LCM(65,84) = 5460
Least Common Multiple (LCM) of 65 and 84 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 65 and 84. First we will calculate the prime factors of 65 and 84.
Prime Factorization of 65
Prime factors of 65 are 5, 13. Prime factorization of 65 in exponential form is:
65 = 51 × 131
Prime Factorization of 84
Prime factors of 84 are 2, 3, 7. Prime factorization of 84 in exponential form is:
84 = 22 × 31 × 71
Now multiplying the highest exponent prime factors to calculate the LCM of 65 and 84.
LCM(65,84) = 51 × 131 × 22 × 31 × 71
LCM(65,84) = 5460