Least Common Multiple of 40/18, 72/23, 105/735

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Know Least Common Multiple of fractions 40/18, 72/23, 105/735 quickly i.e. 2520 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.

Least Common Multiple (LCM) of 40/18, 72/23, 105/735 is 2520.

LCM(40/18, 72/23, 105/735) = 2520

LCM of 40/18, 72/23, 105/735

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

LCM of:

Least Common Multiple of 40/18,72/23,105/735

Given numbers are 40/18,72/23,105/735

Formula to find LCM of Fractions is

LCM = LCM of Numerators/GCF of Denominators

As per the formula LCM of Fractions let’s split into two parts and find the LCM of Numerators and GCF of Denominators

In the given fractions LCM of Numerators means LCM of 40,72,105

Least Common Multiple of Numerators i.e. LCM of 40,72,105 is 2520.

GCF of Denominators means GCF of 18,23,735 as per the given fractions.

GCF of 18,23,735 is 1 as it is the largest common factor for these numbers.

Lets's calculate LCM of 40,72,105

LCM of Fractions 40/18,72/23,105/735 is 2520

2 40, 72, 105
2 20, 36, 105
2 10, 18, 105
3 5, 9, 105
5 5, 3, 35
1, 3, 7

∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 5 x 1 x 3 x 7 = 2520

Least Common Multiple of 40,72,105 with GCF Formula

Least Common Multiple of 40,72,105 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 40,72,105 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(40,72,105) = 1

common factors(in case of two or more numbers have common factors) = 120

GCF(40,72,105) x common factors =1 x 120 = 120

LCM(40,72,105) = ( 40 × 72 × 105 ) / 120

LCM(40,72,105) = 302400 / 120

LCM(40,72,105) = 2520


Lets's calculate GCF of 18,23,735

∴ So GCF of numbers is 1 because of no common factors present between them.

Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 2520/1

Therefore the LCM of Fractions 40/18,72/23,105/735 is 2520

Greatest Common Factor of 18,23,735 By Matching Biggest Common Factor Method

Greatest Common Factor of 18,23,735 By Matching Biggest Common Factor Method

Factors of 18

List of positive integer factors of 18 that divides 18 without a remainder.

1,2,3,6,9,18

Factors of 23

List of positive integer factors of 23 that divides 23 without a remainder.

1,23

Factors of 735

List of positive integer factors of 735 that divides 735 without a remainder.

1,3,5,7,15,21,35,49,105,147,245,735

Greatest Common Factor

We found the factors 18,23,735 . The biggest common factor number is the GCF number.
So the greatest common factor 18,23,735 is 1.


LCM of Fractions Calculation Examples

Here are some samples of LCM of Fractions calculations.

LCM of Fractions Calculation Examples

Here are some samples of LCM of Fractions calculations.

Frequently Asked Questions on Fractional LCM of 40/18, 72/23, 105/735

1. How to find LCM in Fractions?

Answer: LCM of fractions can be found using the simple formula LCM of Fractions = LCM of Numerators/GCF of Denominators.

2. What is the LCM of Fractions for 40/18, 72/23, 105/735?

Answer: LCM of Numerators as per given numbers 40/18, 72/23, 105/735 is

LCM of Numerators i.e. for 40,72,105 is 2520

GCF of denominators i.e. for 18,23,735 is 1.

Thus, LCM of Fractions is 2520.Finally, LCM of Fractions for 40/18, 72/23, 105/735 is 2520.