Question

Find the smallest 5-digit number which is divisible by 21, 28, 36, 45.

Answer 1

find the LCM of the following numbers LCM is 1260 of them so the five digit number is 10080

Answer 2

Let X be the smallest number with the desired properties.

Thus X−9 is the smallest integer divisible by 21,28 36,45

Which implies that X−9 is the lcm of 21,28,36 and 45.

LCM have a distributive property

LCM(21,28,36,45)=LCM(LCM(21,28),LCM(36,45))=LCM(84,180)=1260

Thus

Multiply 1260 by 8 we get our five digit no

X=10080