What is the Least Common Multiple of 548 and 565?
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 548 and 565 is 309620.
LCM(548,565) = 309620
Least Common Multiple of 548 and 565 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 548 and 565, than apply into the LCM equation.
GCF(548,565) = 1
LCM(548,565) = ( 548 × 565) / 1
LCM(548,565) = 309620 / 1
LCM(548,565) = 309620
Least Common Multiple (LCM) of 548 and 565 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 548 and 565. First we will calculate the prime factors of 548 and 565.
Prime Factorization of 548
Prime factors of 548 are 2, 137. Prime factorization of 548 in exponential form is:
548 = 22 × 1371
Prime Factorization of 565
Prime factors of 565 are 5, 113. Prime factorization of 565 in exponential form is:
565 = 51 × 1131
Now multiplying the highest exponent prime factors to calculate the LCM of 548 and 565.
LCM(548,565) = 22 × 1371 × 51 × 1131
LCM(548,565) = 309620
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