Question

Find the smallest number of five digits exactly divisible by 21, 28, 36, 45

Answer 1

First of all we have to find the LCM of these four numbers:

21 = 3 x 7

28 = 2 x 2 x 7

36 = 2 x 2 x 3 x 3

45 = 3 x 3 x 5

LCM = 2 x 2 x 3 x 3 x 5 x 7 = 1260.

Now we have to find the smallest multiple of 1260 which is of five digit.

1260 x 7 = 8820 which is four digit.

1260 x 8 = 10080 which is five digit.

Therefore 10080 is the smallest 5 digit number which is exactly divisible by 21, 28, 36, 45.

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