60,84,96 find the lcm by prime factorization method
Answers
Step-by-step explanation:
Decompose all numbers into prime factors. ...
Write all numbers as the product of its prime factors. Prime factors of 60. ...
Choose the common and uncommon prime factors with the greatest exponent. Common prime factors: 2 , 3. ...
Calculate the Least Common Multiple or LCM.
So, the prime factorisation of 84 is 2 × 2 × 3 × 7 or 22 × 3 × 7, where 2, 3 and 7 are the prime numbers.
We can find the factor in pairs, by multiplying two numbers in a combination to get the result as 60. Let us see the factor pairs of 60.
1 × 60 = 60
2 × 30 = 60
3 × 20 = 60
4 × 15 = 60
5 × 12 = 60
6 × 10 = 60
Therefore, the factors pairs of 60 are (1, 60), (2, 30), (3, 20), (4, 15), (5, 12) and (6, 10).
Factors Of 60
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60
Prime Factorisation of 60
The number 60 is a composite number. Now let us find the prime factors of it.
The first step is to divide the number 60 with the smallest prime factor,i.e. 2.
60 ÷ 2 = 30
Now, check whether 30 can be further divided by 2 or not.
30 ÷ 2 = 15
15 ÷ 2 = 7.5
But, factors cannot be a fraction. Therefore, we will proceed to the next prime number, which is 3.
Now, dividing 15 by 3 we get,
15 ÷ 3 = 5
Again, dividing 5 by 3 will give a fraction number. Therefore, taking the next prime number, 5, into consideration.
5 ÷ 5 = 1
We have received 1 at the end and further, we cannot proceed with the division method, as we know that the multiple of 1 is 1, only. So, the prime factorisation of 60 is 2 × 2 × 3 × 5 or it can be written as 22 × 3 × 5. where 2, 3 and 5 are prime numbers.
Step-by-step explanation:
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