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What is the LCM of $ 14\,and\,42 $ ?
A. $ 7 $
B. $ 14 $
C. $ 1 $
D. $ 42 $

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Last updated date: 22nd Jul 2024
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Answer
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Hint: Least Common Factor (LCM): In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by LCM. It is the smallest positive number that is divisible by both a and b. LCM of two or more than two is not less than any one of them.

Complete step by step solution:
Given,
First number $ = 14 $
Second number $ = 42 $
Now we have to factorize the number
So factor of $ 14 $
 $ \Rightarrow 14 = 2 \times 7 \times 1 $
So factor of $ 42 $
 $ \Rightarrow 42 = 2 \times 3 \times 7 \times 1 $
So the LCM of $ 14\,and\,42 $
 $ \Rightarrow LCM = 2 \times 3 \times 7 \times 1 $
 $ \Rightarrow LCM = 42 $
So the answer is (D) $ 42 $
So, the correct answer is “Option D”.

Note: Highest Common Factor (HCF): It is the greatest common divisor of two or more integers, which will never be zero. The HCF of any two numbers is not greater than two of them. One of the numbers is a prime number is either $ 1 $ or the prime number itself. It is also known as Greatest Common Divisor or Greatest Common Measure.