What is the Least Common Multiple of 549 and 560?
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 549 and 560 is 307440.
LCM(549,560) = 307440
Least Common Multiple of 549 and 560 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 549 and 560, than apply into the LCM equation.
GCF(549,560) = 1
LCM(549,560) = ( 549 × 560) / 1
LCM(549,560) = 307440 / 1
LCM(549,560) = 307440
Least Common Multiple (LCM) of 549 and 560 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 549 and 560. First we will calculate the prime factors of 549 and 560.
Prime Factorization of 549
Prime factors of 549 are 3, 61. Prime factorization of 549 in exponential form is:
549 = 32 × 611
Prime Factorization of 560
Prime factors of 560 are 2, 5, 7. Prime factorization of 560 in exponential form is:
560 = 24 × 51 × 71
Now multiplying the highest exponent prime factors to calculate the LCM of 549 and 560.
LCM(549,560) = 32 × 611 × 24 × 51 × 71
LCM(549,560) = 307440
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