LCM is the least common multiple which is the lowest multiple of two or more numbers.
- For example: find the LCM of 3 and 4 :
3 = 1, 3, 6, 12, 18, 21, 24
4= 1, 4, 8, 12, 16, 20, 24
Since 12 is the smallest common multiple among the 12 and 24, it is considered the L.C.M of 3 and 4.
- Another example :
48 = 2×2×2×2×3 = 24×3
420 = 2×2×3×5×7 = 2² ×3×5×7
L.C.M. of the given numbers = product of all the prime numbers of each of the given number with greatest power (index) of common prime factors. So , LCM will be 24×3×5×7 = 1680
So, to find the LCM follow these steps :
Step 1: List the multiples of the two numbers.
Step 2: Find the multiples common to both numbers.
Step 3: L.C.M. of the given numbers = product of all the prime numbers of each of the given number with greatest power (index) of common prime factors.
H.C.F is the highest common factor which is the largest common factor of two or more numbers.
- Let us consider the numbers 12 and 15. Here are the factors of 12 and 15.
12 = 1, 2, 3, 4, 6, 12
15 = 1,3, 5
So here we can see that the common factors of both 12 and 15 are 1 and 3. But 3 is the largest, so 3 is H.C.F for 12 and 15.
- Now consider the above example :
48 = 2×2×2×2×3 = 24×3
420 = 2×2×3×5×7 = 2² ×3×5×7
H.C.F. of the given numbers = the product of common factors with least power (index). So, it will be 2² ×3 = 12
To find HCF follow these steps :
Step 1: List the factors of two numbers
Step 2: Find the factors common to both numbers.
Step 3: H.C.F. of the given numbers = the product of common factors with least power (index).
Product of two numbers = Their HCF × LCM
Solve this worksheet on HCF and LCM :
- Find the L.C.M. of 72, 240, 196.
- Find the H.C.F. of 72, 126 and 270.
- if the product of two numbers is 84942 and their H.C.F. is 33, find their L.C.M.
- The H.C.F. and L.C.M. of two numbers are 12 and 5040 respectively If one of the numbers is 144, find the other number.
- The product of H.C.F. and L.C.M. of two numbers is 9072. If one of the numbers is 72, find the other number.