What is the Least Common Multiple of 272 and 10320?
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 272 and 10320 is 175440.
LCM(272,10320) = 175440
Least Common Multiple of 272 and 10320 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 272 and 10320, than apply into the LCM equation.
GCF(272,10320) = 16
LCM(272,10320) = ( 272 × 10320) / 16
LCM(272,10320) = 2807040 / 16
LCM(272,10320) = 175440
Least Common Multiple (LCM) of 272 and 10320 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 272 and 10320. First we will calculate the prime factors of 272 and 10320.
Prime Factorization of 272
Prime factors of 272 are 2, 17. Prime factorization of 272 in exponential form is:
272 = 24 × 171
Prime Factorization of 10320
Prime factors of 10320 are 2, 3, 5, 43. Prime factorization of 10320 in exponential form is:
10320 = 24 × 31 × 51 × 431
Now multiplying the highest exponent prime factors to calculate the LCM of 272 and 10320.
LCM(272,10320) = 24 × 171 × 31 × 51 × 431
LCM(272,10320) = 175440
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