find the least number which is exactly divisible by ,14,21,24,42
full solution
Answers
Answer:
168
Step-by-step explanation:
the least no. which is exactly divisible by 14,21,24,42 is 168
Therefore the least number which is exactly divisible by 14, 21, 24, and 42 is 168.
Given:
The numbers: 14, 21, 24, and 42
To Find:
The least possible number is exactly divisible by 14, 21, 24, and 42.
Solution:
The given question can be easily solved as shown below.
The Least number which is exactly divisible by 14, 21, 24, and 42 is nothing but the LCM of given numbers 14, 21, 24, and 42.
The prime factors of '14' = 2 × 7
The prime factors of '21' = 3 × 7
The prime factors of 24 = 2 × 2× 2 × 3
The prime factors of '42' = 2 × 3 × 7
Now to find LCM of 14, 21, 24, and 42, the common prime factors for 21, 24, and 42 are multiplied once and the rest are multiplied as it is. { For example '7' is a common prime factor for 14, 21, and 42 so multiplied only once )
The prime factors of '14' = 2 × 7
The prime factors of '21' = 3 × 7
The prime factors of 24 = 2 × 2× 2 × 3
The prime factors of '42' = 2 × 3 × 7
The underlined prime factors are multiplied only once because they are common prime factors and non-underlined ones are multiplied as it is.
⇒ LCM of 14, 21, 24, and 42 = 2 × 3 × 7 × 2 ×2 = 168
Therefore the least number which is exactly divisible by 14, 21, 24, and 42 is 168.
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