The HCF and LCM of TWO NUMBERS are 9 and 360 respectively. If FIRST NUMBER is 45, FIND THE SECOND NUMBER. [USE THE FORMULA]. HCF=9; LCM=360; "FIRST" NO. =45; "SECOND"NO.=?
Answers
We will learn the relationship between H.C.F. and L.C.M. of two numbers.
First we need to find the highest common factor (H.C.F.) of 15 and 18 which is 3.
Then we need to find the lowest common multiple (L.C.M.) of 15 and 18 which is 90.
H.C.F. × L.C.M. = 3 × 90 = 270
Also the product of numbers = 15 × 18 = 270
Therefore, product of H.C.F. and L.C.M. of 15 and 18 = product of 15 and 18.
Again, let us consider the two numbers 16 and 24
Prime factors of 16 and 24 are:
16 = 2 × 2 × 2 × 2
24 = 2 × 2 × 2 × 3
L.C.M. of 16 and 24 is 48;
H.C.F. of 16 and 24 is 8;
L.C.M. × H.C.F. = 48 × 8 = 384
Product of numbers = 16 × 24 = 384
So, from the above explanations we conclude that the product of highest common factor (H.C.F.) and lowest common multiple (L.C.M.) of two numbers is equal to the product of two numbers
or, H.C.F. × L.C.M. = First number × Second number.