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LCM Formula
When two or more than two numbers have the same digits on the number as their multiples, these numbers are considered communal multiples. Out of all these communal accomplishable multiples, the last, least, or smallest common for both figures is known to be the least common multiple LCM.
The least common multiple formulae help determine the smallest or the least common value for the given set of numbers.
In other words, LCM for some integers says x and y are the least positive integers, which is separable by both x and y.
Formula of LCM
The formula for LCM can be depicted as follows:
LCM = (p x q) / HCF(p, q)
Where,
p and q are two random terms
HCF(p, q) = the highest common multiple of p and q
Methods for Finding out LCM
By Prime Factorization
- Demonstrate each figure as a product of their prime numbers
- LCM will be the product of the utmost power of all factors of prime numbers
By Division Method
- Initially, you must fraction all the presumption numbers by the least or the smallest prime number.
- Then, we must fraction all the presumption numbers by the least prime number.
- We now necessitate writing the quotients and undivided figures or numbers in a fresh line below the premature one.
- Repeat this procedure until we find a phase where no factor of prime numbers is common.
- LCM will be the product of all the divisors and the figures or numbers in the endmost line.
Solved Examples
- Find out the LCM of 8 and 14.
Step 1:
First, write out each number as a product of prime factors.
8 = 2× 2 × 2 = 2³
14 = 2 × 7
Step 2:
Product of the utmost powers of all prime factors.
Here the prime factors are 2 and 7
The highest power of 2 here = 2³
The highest power of 7 here = 7
Hence, LCM = 2³ × 7 = 56
2. If two numbers, 12 and 30, are given. HCF of these two is 6, then find their LCM.
We will use the simple formula of LCM and GCD.
a = 12, b = 30
gcd = 6
Thus, we get the
LCM = a×b / gcd(a, b)
We get,
12 x 30 / 6
= 60
Hence, the LCM is 60.
