# The ratio of two numbers is 3:4 and their HCF is 4 find their LCM..... plzz answer fast with explanation!!!

2
by sainarajput

2015-10-06T21:33:10+05:30
The ratio of two no.s is 3:4. this means that they were cancelled by a  number, say x.
This means that one number is 3x and the other 4x.
This also denotes that gcd(3x,4x)=4.
This means that the product of the commons in the prime fact. of 3x and 4x is 4.
This means that we have to prime factorize 4.
It's 4=2×2.
This means that both 3x and 4x share 2square in their prime factorization.
This says that A number divisible by 3 and 4 is 3x and a number divisible by 4 and has 2 twice when compared to pf(3) is 4x.
Think of such a pair: an example is 12 and 16.
gcd(12,16)=2×2=4
Ha! Here we see hcf of 12 and 16 is 4 and the pair satisfies both conditions.
Now just find lcm.
lcm(12,16)=2⁴×3=16×3=48.

ans=48

2015-10-06T21:57:47+05:30
Ratio is 3:4.
Ratio is obtained after we divide the common divisor, right!!!
The common divisor is the H.C.F., of the two numbers, right!!!
Therefore, 3*4 is a number, and 4*4 is another number.
So, the numbers are, 12 and 16.
L.C.M. of 12 and 16 = H.C.F. of 12 and 16 * remaining multiples, right!!!
12= 4*3
16=4*4
L.C.M. of 12 and 16 = 4*3*4
=48.
Therefore, the L.C.M. is 48.

Thank you.