What is the Least Common Multiple of 282 and 290?
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 282 and 290 is 40890.
LCM(282,290) = 40890
Least Common Multiple of 282 and 290 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 282 and 290, than apply into the LCM equation.
GCF(282,290) = 2
LCM(282,290) = ( 282 × 290) / 2
LCM(282,290) = 81780 / 2
LCM(282,290) = 40890
Least Common Multiple (LCM) of 282 and 290 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 282 and 290. First we will calculate the prime factors of 282 and 290.
Prime Factorization of 282
Prime factors of 282 are 2, 3, 47. Prime factorization of 282 in exponential form is:
282 = 21 × 31 × 471
Prime Factorization of 290
Prime factors of 290 are 2, 5, 29. Prime factorization of 290 in exponential form is:
290 = 21 × 51 × 291
Now multiplying the highest exponent prime factors to calculate the LCM of 282 and 290.
LCM(282,290) = 21 × 31 × 471 × 51 × 291
LCM(282,290) = 40890
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