Find the L.C.M. of 24, 60, and 150 by fundamental theorem of arithmetic.

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answer is A.

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Detailed Solution

Concept- Here, the given numbers will be expressed as the sum of their prime factors. The LCM of the three numbers will then be determined. The result of the most powerful prime factors is LCM, or the lowest common multiple.
Every composite number may be expressed as a unique product of its prime factors, according to the basic theorem of mathematics. A number that is divisible by one and by itself is said to have a prime factor. The provided numbers will first be written as a product of their prime factors. We are aware that the sum of 8 and 3 equals 24. Consequently, we can represent 24 as

The prime number 2's cube is 8. So, we obtain

Now that we are aware of the product of 3, 4, and 5 being 60. Consequently, we can represent 60 as

The square of the prime integer 2 is equal to 4. So, we obtain

Next, we know that 150 is the result of the factors 2, 3, and 25. Consequently, 150 may be written as

The square of the prime number 5 is equal to 25. So, we obtain

Thus,

The greatest power of two is three, the greatest power of 3 is 1, and the greatest power of 5 is 2, as shown in the product of primes. Therefore, 23, 3, and 52 are the prime factors with the highest powers. The combination of the prime components with the highest powers yields the lowest common multiple of the numbers 24, 60, and 150. As a result, we have
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Hence, the correct option is 1.

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