What is the Least Common Multiple of 65 and 70?
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 70 is 910.
LCM(65,70) = 910
Least Common Multiple of 65 and 70 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 70, than apply into the LCM equation.
GCF(65,70) = 5
LCM(65,70) = ( 65 × 70) / 5
LCM(65,70) = 4550 / 5
LCM(65,70) = 910
Least Common Multiple (LCM) of 65 and 70 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 65 and 70. First we will calculate the prime factors of 65 and 70.
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 70
Prime factors of 70 are 2, 5, 7. Prime factorization of 70 in exponential form is:
70 = 21 × 51 × 71
Now multiplying the highest exponent prime factors to calculate the LCM of 65 and 70.
LCM(65,70) = 51 × 131 × 21 × 71
LCM(65,70) = 910