find the lcm by prime factorisation 1. 64,80,100
Answers
LCM of 64 , 80 , 100 is 1600
Given :
The numbers 64 , 80 , 100
To find :
LCM by prime factorisation
Concept :
LCM :
For the given two or more numbers LCM is the least number which is exactly divisible by each of the given numbers
Solution :
Step 1 of 3 :
Write down the given numbers
The given numbers are 64 , 80 , 100
Step 2 of 3 :
Prime factorise the given numbers
64 = 2 × 2 × 2 × 2 × 2 × 2
80 = 2 × 2 × 2 × 2 × 5
100 = 2 × 2 × 5 × 5
Step 3 of 3 :
Find LCM
The required LCM
= 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5
= 1600
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Given:
Three numbers 64, 80, and 100.
To Find:
The LCM of the given three numbers is?
Solution:
1. The LCM of three numbers is defined as the least common number which is multiple for all the three given numbers.
2. Factorise the given numbers into the product of prime numbers.
3. Factorize the number 64,
=> 64 = 2 x 32,
=> 64 = 2 x 2 x 16,
=> 64 = 2 x 2 x 2 x 8,
=> 64 = 2 x 2 x 2 x 2 x 4,
=> 64 = 2 x 2 x 2 x 2 x 2 x 2.
=> 64 = 2^6.
3. Factorize the number 80,
=> 80 = 2 x 40,
=> 80 = 2 x 2 x 20,
=> 80 = 2 x 2 x 2 x 10,
=> 80 = 2 x 2 x 2 x 2 x 5.
=> 80 = 2^4 x 5.
4. Factorize the number 100,
=> 100 = 2 x 50,
=> 100 = 2 x 2 x 25,
=> 100 = 2 x 2 x 5 x 5.
=> 100 = 2² x 5².
5. Hence, the LCM is 2^6 x 5^2,
=> LCM = 64 x 25 = 1600.
Therefore, the LCM of 64, 80, and 100 is 1600.