LCM of Numbers
In this class, We discuss LCM of Numbers.
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LCM – Least Common Multiple
The least number which is exactly divisible by each one of the given numbers is called LCM.
Example:
24, 36
72, 144, we can write infinite numbers.
72 is the least number exactly divisible by 24, 36.
72 is the least common multiple of 24, 36.
Two methods to find the LCM.
1) Factorization
2) Common Division Method
Factorization Method:
24, 36
Write each number in the product of prime factors.
24 = 2^3 * 3
36 = 3^2 * 2^2
LCM = product of highest powers of each factor.
Example 2:
108, 2100
108 = 2^3 * 3^2
2100 = 2^2 * 3 * 5^2 * 7
Product of highest powers of all prime factors = 2^2 * 3^3 * 5^2 * 7
LCM = 18900
Division Method:
The below diagram shows the common division method.
The first division 2 divides into 24. We get 12
2 divides 36, and we get 18.
similarly, we go with common division.
It is not compulsory. All the numbers should be divided.
Take the last before case 2|2,3
Two divided two. We get 1.
Two is not dividing three, so forward the three as it is.
Repeat the division till we get 1’s.
product of all the divisors = LCM
LCM = 2 * 2 * 3 * 2 * 3 = 72.