On this page we have discussed LCM and HCF formulas, definition with examples.
LCM stands for Least Common Factor
LCM or least common factor of two numbers 4, 6 is denoted as LCM(4, 6). And the LCM is the smallest positive integer that is divisible by both 4 and 6, which is 12.
HCF stands for Highest Common Factor
Greated Common Divisor or gcd of two or more positive integers is defined as the largest positive integer that divides the numbers without leaving the remainder.
LCM and HCF Formulas
HCF and LCM FormulaProduct of Two numbers = (HCF of the two numbers) x (LCM of the two numbers)
How to find HCFH.C.F. of Two numbers = Product of Two numbers/L.C.M of two numbers
How to find LCML.C.M of two numbers = Product of Two numbers/H.C.F. of Two numbers
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HCF by Prime Factorization Method
Take an example of finding the highest common factor of 100, 125 and 180. Now let us write the prime factors of 100, 125 and 180. 100 = 2 × 2 × 5 × 5 125 = 5 × 5 × 5 180 = 3 × 3 × 2 × 2 × 5 The common factors of 100, 125 and 180 are 5 Therefore, HCF (100, 125, 180) = 5
HCF by Division Method
Steps to find the HCF of any given numbers:
Larger number/ Smaller Number
The divisor of the above step / Remainder
The divisor of step 2 / remainder. Keep doing this step till R = 0(Zero).
A technique to find the Least Common Multiple (LCM) of a set of numbers by breaking down each number into its prime factors and then multiplying the highest powers of each prime factor.
Lets take two numbers i.e., 25 and 35, now to calculate the LCM:
List the prime factors of each number first. 25 = 5 × 5 35 = 7 × 5
Then multiply each factor the most number of times it occurs in any number.
If the same multiple occurs more than once in both the given numbers, then multiply the factor by the most number of times it occurs. The occurrence of Numbers in the above example: 5: two times 7: one time LCM = 7 × 5 × 5 = 175
LCM by Division Method
Let us see with the same example, which we used to find the LCM using prime factorization. Solve LCM of (25,35) by division method.
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