LCM of 4 and 14 is the smallest number among all common multiples of 4 and 14. The first few multiples of 4 and 14 are (4, 8, 12, 16, 20, 24, 28, . . . ) and (14, 28, 42, 56, 70, . . . ) respectively. There are 3 commonly used methods to find LCM of 4 and 14 - by listing multiples, by division method, and by prime factorization.

You are watching: Least common multiple of 4 and 14

1.LCM of 4 and 14
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM of 4 and 14 is 28.

*

Explanation:

The LCM of two non-zero integers, x(4) and y(14), is the smallest positive integer m(28) that is divisible by both x(4) and y(14) without any remainder.


The methods to find the LCM of 4 and 14 are explained below.

By Listing MultiplesBy Division MethodBy Prime Factorization Method

LCM of 4 and 14 by Listing Multiples

*

To calculate the LCM of 4 and 14 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, 24, 28, . . . ) and 14 (14, 28, 42, 56, 70, . . . . )Step 2: The common multiples from the multiples of 4 and 14 are 28, 56, . . .Step 3: The smallest common multiple of 4 and 14 is 28.

∴ The least common multiple of 4 and 14 = 28.

LCM of 4 and 14 by Division Method

*

To calculate the LCM of 4 and 14 by the division method, we will divide the numbers(4, 14) by their prime factors (preferably common). The product of these divisors gives the LCM of 4 and 14.

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

The LCM of 4 and 14 is the product of all prime numbers on the left, i.e. LCM(4, 14) by division method = 2 × 2 × 7 = 28.

LCM of 4 and 14 by Prime Factorization

Prime factorization of 4 and 14 is (2 × 2) = 22 and (2 × 7) = 21 × 71 respectively. LCM of 4 and 14 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 71 = 28.Hence, the LCM of 4 and 14 by prime factorization is 28.

☛ Also Check:


*


FAQs on LCM of 4 and 14

What is the LCM of 4 and 14?

The LCM of 4 and 14 is 28. To find the LCM of 4 and 14, we need to find the multiples of 4 and 14 (multiples of 4 = 4, 8, 12, 16 . . . . 28; multiples of 14 = 14, 28, 42, 56) and choose the smallest multiple that is exactly divisible by 4 and 14, i.e., 28.

How to Find the LCM of 4 and 14 by Prime Factorization?

To find the LCM of 4 and 14 using prime factorization, we will find the prime factors, (4 = 2 × 2) and (14 = 2 × 7). LCM of 4 and 14 is the product of prime factors raised to their respective highest exponent among the numbers 4 and 14.⇒ LCM of 4, 14 = 22 × 71 = 28.

What is the Relation Between GCF and LCM of 4, 14?

The following equation can be used to express the relation between GCF and LCM of 4 and 14, i.e. GCF × LCM = 4 × 14.

Which of the following is the LCM of 4 and 14? 35, 24, 11, 28

The value of LCM of 4, 14 is the smallest common multiple of 4 and 14. The number satisfying the given condition is 28.

If the LCM of 14 and 4 is 28, Find its GCF.

See more: How To Troubleshoot The Ford Taurus Window Wont Go Up, 2005 Taurus Power Window Problem

LCM(14, 4) × GCF(14, 4) = 14 × 4Since the LCM of 14 and 4 = 28⇒ 28 × GCF(14, 4) = 56Therefore, the greatest common factor = 56/28 = 2.