Relationship between H.C.F. and L.C.M.
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
or, L.C.M. = \(\frac{\textrm{First Number} \times \textrm{Second Number}}{\textrm{H.C.F.}}\)
or, L.C.M. × H.C.F. = Product of two given numbers
or, L.C.M. = \(\frac{\textrm{Product of Two Given Numbers}}{\textrm{H.C.F.}}\)
or, H.C.F. = \(\frac{\textrm{Product of Two Given Numbers}}{\textrm{L.C.M.}}\)
Solved examples on the
relationship between H.C.F. and L.C.M.:
1. Find the
L.C.M. of 1683 and 1584.
Solution:
First we find highest common
factor of 1683 and 1584
Therefore, highest common factor of 1683 and 1584 = 99
Lowest common multiple of 1683 and 1584 = First number ×
Second number/ H.C.F.
= \(\frac{1584 × 1683}{99}\)
= 26928
2. Highest common
factor and lowest common multiple of two numbers are 18 and 1782 respectively.
One number is 162, find the other.
Solution:
We know, H.C.F. × L.C.M. = First number × Second number then
we get,
18 × 1782 = 162 × Second number
\(\frac{18 × 1782}{162}\) = Second number
Therefore, the second number = 198
3. The HCF of two numbers is 3 and their LCM is 54. If one of
the numbers is 27, find the other number.
Solution:
HCF × LCM = Product of two numbers
3 × 54 = 27 × second number
Second number = \(\frac{3 × 54}{27}\)
Second number = 6
4. The highest common factor and the lowest common multiple of two numbers are 825 and 25 respectively. If one of the two numbers is 275, find the other number.
Solution:
We know, H.C.F. × L.C.M. = First number × Second number then we get,
825 × 25 = 275 × Second number
\(\frac{825 × 25}{275}\) = Second number
Therefore, the second number = 75
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● Multiples.
Common Multiples.
Least Common Multiple (L.C.M).
To find Least Common Multiple by using Prime Factorization Method.
Examples to find Least Common Multiple by using Prime Factorization Method.
To Find Lowest Common Multiple by using Division Method
Examples to find Least Common Multiple of two numbers by using Division Method
Examples to find Least Common Multiple of three numbers by using Division Method
Relationship between H.C.F. and L.C.M.
Worksheet on H.C.F. and L.C.M.
Word problems on H.C.F. and L.C.M.
Worksheet on word problems on H.C.F. and L.C.M.
5th Grade Math Problems
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