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Find the L.C.M of \[39,65,130,156\]

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Last updated date: 25th Feb 2024
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IVSAT 2024
Answer
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Hint: To find the lowest common multiple LCM for the given numbers we will use prime factorization method. It is the method to express the given number as the product of prime factors. From all the received prime factors after applying prime factorization to the given number, identify the maximum number of times each prime factor appears. This is the LCM or least common multiple.

Complete step-by-step answer:
We know the prime factorization method is the splitting of a given number in terms of prime factors. Prime factors or numbers are factors that are divided exactly by themselves or 1, for example 2, 3, 5, 7, 11, 13 etc.
Using prime factorization method
(1). \[39,65,130,156\]
Factor of \[39=3\times 13\]. . . . . . . . . . . . . .. . . . . . . . . (1)
Factor of \[65=5\times 13\]. . . . . . . . . . . . . . . . . . . . . . . (2)
Factor of \[130=2\times 5\times 13\]. . . . . . . . . . . . . . . . . . . (3)
Factor of \[156=2\times 2\times 3\times 13\]. . . . . . . . . . . . . . . . . (4)
We have to take the maximum number of times each prime factor appears; this is the least common multiple or else called as L.C.M of the given numbers.
\[L.C.M\left( 39,65,130,156 \right)=2\times 2\times 3\times 5\times 13=780\]

Note: The only possible mistake you could encounter can be the use of common factors in the prime factorization method instead of prime factors. Only use prime factors and perform prime factorization carefully.