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Calculation Of The Least Common Multiple Of 10 And 25, Least Common Multiple Of 10 And 25

LCM of 10 and 25 is the smallest number among all common multiples of 10 and 25. The first few multiples of 10 and 25 are (10, 20, 30, 40, 50, 60, . . . ) and (25, 50, 75, 100, 125, 150, . . . ) respectively. There are 3 commonly used methods to find LCM of 10 and 25 – by listing multiples, by division method, and by prime factorization.

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1. LCM of 10 and 25
2. List of Methods
3. Solved Examples
4. FAQs

Answer: LCM of 10 and 25 is 50.

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Explanation:

The LCM of two non-zero integers, x(10) and y(25), is the smallest positive integer m(50) that is divisible by both x(10) and y(25) without any remainder.

Let's look at the different methods for finding the LCM of 10 and 25.

By Prime Factorization MethodBy Division MethodBy Listing Multiples

LCM of 10 and 25 by Prime Factorization

Prime factorization of 10 and 25 is (2 × 5) = 21 × 51 and (5 × 5) = 52 respectively. LCM of 10 and 25 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 52 = 50.Hence, the LCM of 10 and 25 by prime factorization is 50.

LCM of 10 and 25 by Division Method

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To calculate the LCM of 10 and 25 by the division method, we will divide the numbers(10, 25) by their prime factors (preferably common). The product of these divisors gives the LCM of 10 and 25.

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Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 10 and 25 is the product of all prime numbers on the left, i.e. LCM(10, 25) by division method = 2 × 5 × 5 = 50.

LCM of 10 and 25 by Listing Multiples

To calculate the LCM of 10 and 25 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 10 (10, 20, 30, 40, 50, 60, . . . ) and 25 (25, 50, 75, 100, 125, 150, . . . . )Step 2: The common multiples from the multiples of 10 and 25 are 50, 100, . . .Step 3: The smallest common multiple of 10 and 25 is 50.

∴ The least common multiple of 10 and 25 = 50.

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FAQs on LCM of 10 and 25

What is the LCM of 10 and 25?

The LCM of 10 and 25 is 50. To find the LCM (least common multiple) of 10 and 25, we need to find the multiples of 10 and 25 (multiples of 10 = 10, 20, 30, 40 . . . . 50; multiples of 25 = 25, 50, 75, 100) and choose the smallest multiple that is exactly divisible by 10 and 25, i.e., 50.

What are the Methods to Find LCM of 10 and 25?

The commonly used methods to find the LCM of 10 and 25 are:

Prime Factorization MethodListing MultiplesDivision Method

Which of the following is the LCM of 10 and 25? 50, 12, 21, 10

The value of LCM of 10, 25 is the smallest common multiple of 10 and 25. The number satisfying the given condition is 50.

What is the Relation Between GCF and LCM of 10, 25?

The following equation can be used to express the relation between GCF and LCM of 10 and 25, i.e. GCF × LCM = 10 × 25.

If the LCM of 25 and 10 is 50, Find its GCF.

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LCM(25, 10) × GCF(25, 10) = 25 × 10Since the LCM of 25 and 10 = 50⇒ 50 × GCF(25, 10) = 250Therefore, the GCF (greatest common factor) = 250/50 = 5.

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