Question

Identify the least number that is exactly divisible by 24, 28, 36 and 48.
1004 1008 1012 1016

Answer 1

1008

1008 is divisible by 24 , 28, 36 , 48

• 1008 ÷ 24 = 42

• 1008 ÷ 28 = 36

• 1008 ÷ 36 = 28

• 1008 ÷ 48 = 21

Answer 2

Given :  Number exactly divisible by 24, 28,36,48​

To Find : Least Number

Solution:

To find least number exactly divisible by 24, 28,36,48​

Need to find LCM ( 24 , 28 , 36 , 48)

LCM  - Least common multiplier of given numbers is the least number which is perfectly divisible by given numbers.

LCM = product of each factor  of highest power

24 = 2 * 2 * 2 * 3  = 2³ * 3¹

28 = 2 * 2 * 7  = 2² * 7¹

36 = 2 * 2 * 3 * 3 = 2² * 3²

48 = 2 * 2 * 2 * 2 * 3 = 2⁴ * 3¹

LCM = 2⁴ * 3² * 7¹

= 16 * 9 * 7

=  144 * 7

= 1008

1008 is the  least number exactly divisible by 24, 28,36,48​

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