What is the Least Common Multiple of 52 and 65?
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 52 and 65 is 260.
LCM(52,65) = 260
Least Common Multiple of 52 and 65 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 52 and 65, than apply into the LCM equation.
GCF(52,65) = 13
LCM(52,65) = ( 52 × 65) / 13
LCM(52,65) = 3380 / 13
LCM(52,65) = 260
Least Common Multiple (LCM) of 52 and 65 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 52 and 65. First we will calculate the prime factors of 52 and 65.
Prime Factorization of 52
Prime factors of 52 are 2, 13. Prime factorization of 52 in exponential form is:
52 = 22 × 131
Prime Factorization of 65
Prime factors of 65 are 5, 13. Prime factorization of 65 in exponential form is:
65 = 51 × 131
Now multiplying the highest exponent prime factors to calculate the LCM of 52 and 65.
LCM(52,65) = 22 × 131 × 51
LCM(52,65) = 260