LCM that 15 and also 24 is the the smallest number amongst all typical multiples of 15 and 24. The first few multiples the 15 and also 24 are (15, 30, 45, 60, 75, . . . ) and (24, 48, 72, 96, 120, 144, . . . ) respectively. There space 3 generally used techniques to uncover LCM of 15 and also 24 - by division method, by prime factorization, and by listing multiples.

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1.LCM the 15 and 24
2.List the Methods
3.Solved Examples
4.FAQs

Answer: LCM the 15 and also 24 is 120.

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Explanation:

The LCM of two non-zero integers, x(15) and y(24), is the smallest positive integer m(120) the is divisible through both x(15) and y(24) without any kind of remainder.


The methods to find the LCM the 15 and 24 are explained below.

By department MethodBy prime Factorization MethodBy Listing Multiples

LCM of 15 and also 24 by department Method

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To calculation the LCM the 15 and also 24 through the department method, we will certainly divide the numbers(15, 24) by your prime factors (preferably common). The product of these divisors provides the LCM of 15 and 24.

Step 3: continue the measures until just 1s space left in the critical row.

The LCM the 15 and also 24 is the product of every prime numbers on the left, i.e. LCM(15, 24) by department method = 2 × 2 × 2 × 3 × 5 = 120.

LCM of 15 and 24 by element Factorization

Prime administer of 15 and also 24 is (3 × 5) = 31 × 51 and also (2 × 2 × 2 × 3) = 23 × 31 respectively. LCM of 15 and also 24 have the right to be acquired by multiply prime components raised to your respective highest power, i.e. 23 × 31 × 51 = 120.Hence, the LCM that 15 and 24 by element factorization is 120.

LCM the 15 and also 24 by Listing Multiples

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To calculation the LCM the 15 and 24 by listing the end the typical multiples, we deserve to follow the given listed below steps:

Step 1: perform a couple of multiples that 15 (15, 30, 45, 60, 75, . . . ) and 24 (24, 48, 72, 96, 120, 144, . . . . )Step 2: The usual multiples from the multiples of 15 and 24 room 120, 240, . . .Step 3: The smallest usual multiple the 15 and 24 is 120.

∴ The least typical multiple that 15 and also 24 = 120.

☛ additionally Check:


Example 3: Verify the relationship in between GCF and also LCM of 15 and also 24.

Solution:

The relation in between GCF and LCM of 15 and 24 is provided as,LCM(15, 24) × GCF(15, 24) = Product of 15, 24Prime administer of 15 and 24 is offered as, 15 = (3 × 5) = 31 × 51 and 24 = (2 × 2 × 2 × 3) = 23 × 31LCM(15, 24) = 120GCF(15, 24) = 3LHS = LCM(15, 24) × GCF(15, 24) = 120 × 3 = 360RHS = Product that 15, 24 = 15 × 24 = 360⇒ LHS = RHS = 360Hence, verified.


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FAQs top top LCM that 15 and also 24

What is the LCM the 15 and 24?

The LCM that 15 and also 24 is 120. To discover the LCM (least typical multiple) that 15 and also 24, we need to discover the multiples that 15 and also 24 (multiples that 15 = 15, 30, 45, 60 . . . . 120; multiples the 24 = 24, 48, 72, 96 . . . . 120) and also choose the the smallest multiple that is precisely divisible by 15 and also 24, i.e., 120.

How to find the LCM the 15 and 24 by element Factorization?

To discover the LCM of 15 and also 24 using prime factorization, us will uncover the prime factors, (15 = 3 × 5) and (24 = 2 × 2 × 2 × 3). LCM of 15 and 24 is the product the prime factors raised to your respective highest possible exponent among the numbers 15 and also 24.⇒ LCM of 15, 24 = 23 × 31 × 51 = 120.

What room the methods to uncover LCM the 15 and also 24?

The typically used methods to discover the LCM that 15 and 24 are:

Listing MultiplesPrime administer MethodDivision Method

What is the least Perfect Square Divisible through 15 and also 24?

The least number divisible through 15 and also 24 = LCM(15, 24)LCM of 15 and also 24 = 2 × 2 × 2 × 3 × 5 ⇒ least perfect square divisible by each 15 and also 24 = LCM(15, 24) × 2 × 3 × 5 = 3600 Therefore, 3600 is the forced number.

If the LCM that 24 and 15 is 120, uncover its GCF.

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LCM(24, 15) × GCF(24, 15) = 24 × 15Since the LCM of 24 and also 15 = 120⇒ 120 × GCF(24, 15) = 360Therefore, the GCF (greatest usual factor) = 360/120 = 3.