Question

The ratio between two numbers is 3:4 and their Lcm is 180. The first number is _______???

Answer 1

Let the 2 numbers be 3x and 4x and HCF be x.

Using formula, a×b = LCM × HCF

3x × 4x = 180 × x
12x² = 180x
x = 180/12
x = 15

a = 3x = 3×15 = 45
b = 4x = 4×15 = 60
HCF = x = 15

Hope this helps :)

Answer 2

Always remember this formula which i am about to tell you.

This can come in handy sometimes:

1) LCM=a * b * HCF where a and b are the ratio:

therefore HCF =180/12=15

Now,you have the HCF of the given ratio

To find the two numbers you have to use another formula which is :

2) a * HCF=original number (where a is the numerator in the ratio given)

b * HCF=original number (b is the denominator)

Now you understand why i find HCF of the two numbers at first:

First number =3 * 15=45

Second Number =4 * 14=60

Hope this helps :)