LCM that 14 and also 49 is the the smallest number amongst all usual multiples the 14 and also 49. The first couple of multiples of 14 and 49 space (14, 28, 42, 56, . . . ) and (49, 98, 147, 196, 245, 294, . . . ) respectively. There space 3 generally used methods to discover LCM of 14 and also 49 - by listing multiples, by department method, and by element factorization.

You are watching: Least common multiple of 14 and 49

1.LCM the 14 and 49
2.List the Methods
3.Solved Examples
4.FAQs

Answer: LCM the 14 and also 49 is 98.

*

Explanation:

The LCM of two non-zero integers, x(14) and also y(49), is the smallest hopeful integer m(98) the is divisible by both x(14) and y(49) without any kind of remainder.


Let's look in ~ the various methods because that finding the LCM of 14 and also 49.

By element Factorization MethodBy Listing MultiplesBy division Method

LCM the 14 and also 49 by prime Factorization

Prime administrate of 14 and 49 is (2 × 7) = 21 × 71 and (7 × 7) = 72 respectively. LCM that 14 and 49 deserve to be derived by multiply prime components raised to your respective greatest power, i.e. 21 × 72 = 98.Hence, the LCM the 14 and 49 by prime factorization is 98.

LCM that 14 and 49 through Listing Multiples

*

To calculate the LCM that 14 and 49 by listing out the common multiples, we have the right to follow the given below steps:

Step 1: list a couple of multiples the 14 (14, 28, 42, 56, . . . ) and 49 (49, 98, 147, 196, 245, 294, . . . . )Step 2: The common multiples from the multiples that 14 and 49 space 98, 196, . . .Step 3: The smallest usual multiple that 14 and 49 is 98.

∴ The least common multiple of 14 and 49 = 98.

LCM of 14 and also 49 by division Method

*

To calculation the LCM that 14 and also 49 by the division method, we will certainly divide the numbers(14, 49) by their prime determinants (preferably common). The product of these divisors gives the LCM the 14 and 49.

Step 3: proceed the actions until just 1s space left in the critical row.

The LCM that 14 and also 49 is the product of all prime number on the left, i.e. LCM(14, 49) by department method = 2 × 7 × 7 = 98.

☛ also Check:


*


FAQs top top LCM that 14 and 49

What is the LCM that 14 and also 49?

The LCM that 14 and 49 is 98. To discover the LCM (least common multiple) that 14 and also 49, we require to discover the multiples of 14 and also 49 (multiples of 14 = 14, 28, 42, 56 . . . . 98; multiples of 49 = 49, 98, 147, 196) and also choose the smallest multiple that is precisely divisible by 14 and also 49, i.e., 98.

How to uncover the LCM the 14 and also 49 by prime Factorization?

To uncover the LCM of 14 and 49 making use of prime factorization, us will find the element factors, (14 = 2 × 7) and (49 = 7 × 7). LCM that 14 and also 49 is the product the prime components raised to your respective greatest exponent among the number 14 and 49.⇒ LCM that 14, 49 = 21 × 72 = 98.

What is the the very least Perfect Square Divisible by 14 and 49?

The the very least number divisible by 14 and 49 = LCM(14, 49)LCM of 14 and also 49 = 2 × 7 × 7 ⇒ the very least perfect square divisible by each 14 and also 49 = LCM(14, 49) × 2 = 196 Therefore, 196 is the required number.

What are the approaches to find LCM of 14 and 49?

The typically used approaches to find the LCM the 14 and 49 are:

Listing MultiplesDivision MethodPrime factorization Method

If the LCM that 49 and 14 is 98, uncover its GCF.

See more: Describe The Job Of An Ethnomusicologist : Career And Salary Facts

LCM(49, 14) × GCF(49, 14) = 49 × 14Since the LCM of 49 and also 14 = 98⇒ 98 × GCF(49, 14) = 686Therefore, the GCF (greatest common factor) = 686/98 = 7.