Interesting Facts about LCM (original) (raw)

Last Updated : 23 Jul, 2025

**LCM (Least Common Multiple) of two or more numbers is the smallest number that is divisible by each of the given numbers (resulting in a remainder of 0 when we divide the LCM by the given numbers).

To find the LCM of 3 and 5, we list the multiples of both numbers:

• Multiples of 3: 3, 6, 9, 12, **15, 18, . . .
• Multiples of 5: 5, 10, **15, 20, 25, . . .

By comparing the multiples of 3 and 5, we find that the lowest number that is a multiple of both 3 and 5 is **15. Thus, the LCM of 3 and 5 is **15.

Some of the important facts on to LCM ( Least Common Multiple) are:

• The LCM of any number and 1 is always the number itself, as 1 is a factor of every integer.
• When calculating the LCM of two prime numbers, the result is simply their product since prime numbers doesn't share any common factors other than 1.
• LCM (Least Common Multiple) of a number and its multiple is multiple itself, as it is the smallest multiple that both the number and the multiple share.
• If two numbers are coprime (having no common factors other than 1), their LCM is equal to their product.
• The LCM of two consecutive integers is always their product, as consecutive integers share no common factors other than 1.
• For more than two numbers, the LCM can be calculated sequentially, starting with the first two numbers and then incorporating the next number, using the formula:
  • LCM (a, b, c) = LCM (LCM (a, b), c).
• LCM of the first 10 natural numbers is **2520.
• LCM is always greater than or equal to the largest number in a problem.
• The product of GCD and LCM of two natural numbers is always equal to the product of numbers i.e., **LCM (a, b) × GCD (a, b) = a × b.
• LCM is always divisible by GCD.
• The LCM of an EVEN number and another EVEN will always be even.
• The LCM of an ODD number and EVEN number will always be even.
• If two numbers are factors and multiples of each other, the smaller number is the HCF (Highest Common Factor), and the larger number is the LCM (Least Common Multiple).
• The HCF (Highest Common Factor) of two or more numbers is always a factor of their LCM (Least Common Multiple).
• To find the LCM of fractions, you calculate the LCM of the numerators and divide it by the HCF of the denominators.
• GCD and LCM distribute over each other.
  GCD(a, LCM(b, c)) = GCD(LCM(a, b), LCM(a, c)) and
  LCM(a, GCD(b, c)) = LCM(GCD(a, b), GCD(a, c))

**Also Read,

• **Interesting Facts about Prime Numbers
• **Interesting Facts about Number 37
• **Interesting Facts about GCD