LCM of 4, 6, and 10

LCM of 4, 6, and 10 is the smallest number among all common multiples of 4, 6, and 10. The first few multiples of 4, 6, and 10 are (4, 8, 12, 16, 20 . . .), (6, 12, 18, 24, 30 . . .), and (10, 20, 30, 40, 50 . . .) respectively. There are 3 commonly used methods to find LCM of 4, 6, 10 – by listing multiples, by prime factorization, and by division method.

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1. LCM of 4, 6, and 10 2. List of Methods 3. Solved Examples 4. FAQs

**Answer:** LCM of 4, 6, and 10 is 60.

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**Explanation: **

The LCM of three non-zero integers, a(4), b(6), and c(10), is the smallest positive integer m(60) that is divisible by a(4), b(6), and c(10) without any remainder.

Let’s look at the different methods for finding the LCM of 4, 6, and 10.

- By Listing Multiples
- By Division Method
- By Prime Factorization Method

### LCM of 4, 6, and 10 by Listing Multiples

To calculate the LCM of 4, 6, 10 by listing out the common multiples, we can follow the given below steps:

**Step 1:**List a few multiples of 4 (4, 8, 12, 16, 20 . . .), 6 (6, 12, 18, 24, 30 . . .), and 10 (10, 20, 30, 40, 50 . . .).**Step 2:**The common multiples from the multiples of 4, 6, and 10 are 60, 120, . . .**Step 3:**The smallest common multiple of 4, 6, and 10 is 60.

∴ The least common multiple of 4, 6, and 10 = 60.

### LCM of 4, 6, and 10 by Division Method

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To calculate the LCM of 4, 6, and 10 by the division method, we will divide the numbers(4, 6, 10) by their prime factors (preferably common). The product of these divisors gives the LCM of 4, 6, and 10.

**Step 1:**Find the smallest prime number that is a factor of at least one of the numbers, 4, 6, and 10. Write this prime number(2) on the left of the given numbers(4, 6, and 10), separated as per the ladder arrangement.**Step 2:**If any of the given numbers (4, 6, 10) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.**Step 3:**Continue the steps until only 1s are left in the last row.

The LCM of 4, 6, and 10 is the product of all prime numbers on the left, i.e. LCM(4, 6, 10) by division method = 2 × 2 × 3 × 5 = 60.

### LCM of 4, 6, and 10 by Prime Factorization

Prime factorization of 4, 6, and 10 is (2 × 2) = 22, (2 × 3) = 21 × 31, and (2 × 5) = 21 × 51 respectively. LCM of 4, 6, and 10 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 31 × 51 = 60. Hence, the LCM of 4, 6, and 10 by prime factorization is 60.

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- LCM of 12, 16 and 20 – 240
- LCM of 10, 12 and 15 – 60
- LCM of 50 and 48 – 1200
- LCM of 20 and 32 – 160
- LCM of 2, 5 and 7 – 70
- LCM of 7, 8 and 9 – 504
- LCM of 4, 12, 16 and 24 – 48