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Least Common Multiple of 6/75, 14/120, 15/200

Know Least Common Multiple of fractions 6/75, 14/120, 15/200 quickly i.e. 42 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.

Least Common Multiple (LCM) of 6/75, 14/120, 15/200 is 42.

LCM(6/75, 14/120, 15/200) = 42

LCM of 6/75, 14/120, 15/200

Enter two or more fractions separated by "commas"

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

LCM of:

Given numbers are 6/75,14/120,15/200

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 6,14,15

Least Common Multiple of Numerators i.e. LCM of 6,14,15 is 210.

GCF of Denominators means GCF of 75,120,200 as per the given fractions.

GCF of 75,120,200 is 5 as it is the largest common factor for these numbers.

Lets's calculate LCM of 6,14,15

Least Common Multiple (LCM) of 6,14,15 By Common Division

2 6, 14, 15
3 3, 7, 15
1, 7, 5

∴ So the LCM of the given numbers is 2 x 3 x 1 x 7 x 5 = 210

Least Common Multiple of 6,14,15 with GCF Formula

Least Common Multiple of 6,14,15 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 6,14,15 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(6,14,15) = 1

common factors(in case of two or more numbers have common factors) = 6

GCF(6,14,15) x common factors =1 x 6 = 6

LCM(6,14,15) = ( 6 × 14 × 15 ) / 6

LCM(6,14,15) = 1260 / 6

LCM(6,14,15) = 210


Lets's calculate GCF of 75,120,200

Greatest Common Factor (GCF) of 75,120,200 By Common Division

5 75, 120, 200
15, 24, 40

∴ So the GCF of the given numbers is 5 = 5

Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 210/5

Therefore the LCM of Fractions 6/75,14/120,15/200 is 42

Greatest Common Factor of 75,120,200 By Matching Biggest Common Factor Method

Greatest Common Factor of 75,120,200 By Matching Biggest Common Factor Method

Factors of 75

List of positive integer factors of 75 that divides 75 without a remainder.

1,3,5,15,25,75

Factors of 120

List of positive integer factors of 120 that divides 120 without a remainder.

1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

Factors of 200

List of positive integer factors of 200 that divides 200 without a remainder.

1,2,4,5,8,10,20,25,40,50,100,200

Greatest Common Factor

We found the factors 75,120,200 . The biggest common factor number is the GCF number.
So the greatest common factor 75,120,200 is 5.


LCM of Fractions Calculation Examples

Frequently Asked Questions on Fractional LCM of 6/75, 14/120, 15/200

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 6/75, 14/120, 15/200?

Answer: LCM of Numerators as per given numbers 6/75, 14/120, 15/200 is

LCM of Numerators i.e. for 6,14,15 is 210

GCF of denominators i.e. for 75,120,200 is 5.

Thus, LCM of Fractions is 42.Finally, LCM of Fractions for 6/75, 14/120, 15/200 is 42.