How can we find LCM and HCF of fractions
How can we find LCM and HCF of fractions
Let’s take two fractions (a/b) and (c/d).
To find LCM and HCF of (a/b) and (c/d) the generalized formula will be:
H.C.F = H.C.F of numerators / L.C.M of denominators
L.C.M = L.C.M of numerators / H.C.F of denominators
Now L.C.M of two numbers is the smallest number (not zero) that is a multiple of both. Eg: L.C.M of 12,15:
The multiples of 12 are : 12, 24, 36, 48, 60, 72, 84, ....
The multiples of 15 are : 15, 30, 45, 60, 75, 90, ....
60 is a common multiple (a multiple of both 12 and 15), and there are no lower common multiples.
Therefore, the lowest common multiple(L.C.M) of 12 and 15 is 60.
H.C.F of two numbers is the largest whole number which is a factor of both. Eg: H.C.F of 12,15:
The factors of 12 are : 1, 2, 3, 4, 6, 12.
The factors of 15 are : 1, 3, 5, 15.
1 and 3 are the only common factors (numbers which are factors of both 12 and 15).
Therefore, the highest common factor of 12 and 15 is 3.
Now,to find out the LCM and HCF of fractions .
Let’s take example of (4/5) & (3/7):
LCM=lcm of (4,3)/hcf of (5,7) = 12/1 = 12 (Since 12 is the least number that comes in table of both 4,3 and 1 is the greatest number that can divide both 5,7).
HCF=hcf of (4,3)/lcm of (5,7) = 1/35 (Since 1 is the greatest number that can divide both 4,3 and 35 is the smallest number that comes in table of both 5,7).
I hope you get it!
Let’s take two fractions (a/b) and (c/d).
To find LCM and HCF of (a/b) and (c/d) the generalized formula will be:
H.C.F = H.C.F of numerators / L.C.M of denominators
L.C.M = L.C.M of numerators / H.C.F of denominators
Now L.C.M of two numbers is the smallest number (not zero) that is a multiple of both. Eg: L.C.M of 12,15:
The multiples of 12 are : 12, 24, 36, 48, 60, 72, 84, ....
The multiples of 15 are : 15, 30, 45, 60, 75, 90, ....
60 is a common multiple (a multiple of both 12 and 15), and there are no lower common multiples.
Therefore, the lowest common multiple(L.C.M) of 12 and 15 is 60.
H.C.F of two numbers is the largest whole number which is a factor of both. Eg: H.C.F of 12,15:
The factors of 12 are : 1, 2, 3, 4, 6, 12.
The factors of 15 are : 1, 3, 5, 15.
1 and 3 are the only common factors (numbers which are factors of both 12 and 15).
Therefore, the highest common factor of 12 and 15 is 3.
Now,to find out the LCM and HCF of fractions .
Let’s take example of (4/5) & (3/7):
LCM=lcm of (4,3)/hcf of (5,7) = 12/1 = 12 (Since 12 is the least number that comes in table of both 4,3 and 1 is the greatest number that can divide both 5,7).
HCF=hcf of (4,3)/lcm of (5,7) = 1/35 (Since 1 is the greatest number that can divide both 4,3 and 35 is the smallest number that comes in table of both 5,7).
I hope you get it!
