What is the least common multiple of 40 35 and 18?

Answer 1

Find LCM (40,35,18).

40 = 2 x 2 x 2 x 5

35 = 5 x 7

18 = 2 x 3 x 3

GCF(40,35) = 5

LCM(40,35,18) = LCM(LCM(40,35),18)

LCM(40,35) = (40 x 35) / GCF(40,35)

LCM(40,35) = 1400 / 5

LCM(40,35) = 280

LCM(40,35,18) = LCM(280,18)

280 = 2 x 2 x 2 x 5 x 7

18 = 2 x 3 x 3

GCF(280,18) = 2

LCM(280,18) = (280 x 18)/GCF(280,18)

LCM(280,18) = 5040 / 2

LCM(280,18) = 2520

LCM(40,35,18) = 2520

If you have time, check to make sure that this is the true LCM. Here's how to do it.

Divide 2,520 by 40, 35, and 18.

2520/40 = 63

2520/35 = 72

2520/18 = 140

If this is the true LCM, then these three numbers you get (63, 72, and 140) will have a GCF of 1.

63 = 3 x 3 x 7

72 = 3 x 3 x 2 x 2 x 2

140 = 2 x 2 x 5 x 7

GCF(63,72,140) =? 1

1 = 1

2,520 is indeed the true LCM.