What is the Least Common Multiple of 240 and 253?
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 240 and 253 is 60720.
LCM(240,253) = 60720
Least Common Multiple of 240 and 253 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 240 and 253, than apply into the LCM equation.
GCF(240,253) = 1
LCM(240,253) = ( 240 × 253) / 1
LCM(240,253) = 60720 / 1
LCM(240,253) = 60720
Least Common Multiple (LCM) of 240 and 253 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 240 and 253. First we will calculate the prime factors of 240 and 253.
Prime Factorization of 240
Prime factors of 240 are 2, 3, 5. Prime factorization of 240 in exponential form is:
240 = 24 × 31 × 51
Prime Factorization of 253
Prime factors of 253 are 11, 23. Prime factorization of 253 in exponential form is:
253 = 111 × 231
Now multiplying the highest exponent prime factors to calculate the LCM of 240 and 253.
LCM(240,253) = 24 × 31 × 51 × 111 × 231
LCM(240,253) = 60720
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