Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Know Least Common Multiple of fractions 78/65, 72/74, 668/765 quickly i.e. 156312 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.
Least Common Multiple (LCM) of 78/65, 72/74, 668/765 is 156312.
LCM(78/65, 72/74, 668/765) = 156312
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given numbers are 78/65,72/74,668/765
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 78,72,668
Least Common Multiple of Numerators i.e. LCM of 78,72,668 is 156312.
GCF of Denominators means GCF of 65,74,765 as per the given fractions.
GCF of 65,74,765 is 1 as it is the largest common factor for these numbers.
Lets's calculate LCM of 78,72,668
2 | 78, 72, 668 |
2 | 39, 36, 334 |
3 | 39, 18, 167 |
13, 6, 167 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 13 x 6 x 167 = 156312
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 78,72,668 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,72,668) = 2
common factors(in case of two or more numbers have common factors) = 12
GCF(78,72,668) x common factors =2 x 12 = 24
LCM(78,72,668) = ( 78 × 72 × 668 ) / 24
LCM(78,72,668) = 3751488 / 24
LCM(78,72,668) = 156312
Lets's calculate GCF of 65,74,765
∴ So GCF of numbers is 1 because of no common factors present between them.
Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 156312/1
Therefore the LCM of Fractions 78/65,72/74,668/765 is 156312
Factors of 65
List of positive integer factors of 65 that divides 65 without a remainder.
1,5,13,65
Factors of 74
List of positive integer factors of 74 that divides 74 without a remainder.
1,2,37,74
Factors of 765
List of positive integer factors of 765 that divides 765 without a remainder.
1,3,5,9,15,17,45,51,85,153,255,765
Greatest Common Factor
We found the factors 65,74,765 . The biggest common factor number is the GCF number.
So the greatest common factor 65,74,765 is 1.
Here are some samples of LCM of Fractions calculations.
Here are some samples of LCM of Fractions calculations.
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 78/65, 72/74, 668/765?
Answer: LCM of Numerators as per given numbers 78/65, 72/74, 668/765 is
LCM of Numerators i.e. for 78,72,668 is 156312
GCF of denominators i.e. for 65,74,765 is 1.
Thus, LCM of Fractions is 156312.Finally, LCM of Fractions for 78/65, 72/74, 668/765 is 156312.