find HCF and LCM of 12,63 and 99
using prime factorization method
Answers
Answer:
Concept:
The acronym LCM means least common multiple. When you multiply a number by a whole number, you obtain a multiple (greater than 0). A factor is a number that is produced when a whole number is multiplied by another number.
The greatest number that divides each of the two or more numbers is known as the HCF, or the highest common factor. The Greatest Common Measure (GCM) and Greatest Common Divisor are further names for HCF (GCD).
Step-by-step explanation:
Prime factorization is a process of factoring a number in terms of prime numbers i.e. the factors will be prime numbers.
LCM of 12, 63, and 99
12 = 2 × 2 × 3
63 = 3 × 3 × 7
99 = 3 × 3 × 11
LCM of 12, 63, and 99 = 2 × 3 × 3 × 7 × 3 × 11
= 4158
HCF of 12, 63, and 99 = 3 × 4 × 7 × 11
= 924
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Concept:
HCF- Highest Common Factor: It refers to the highest common number by which all the given numbers can be divided.
LCM- Lowest Common Multiple: It refers to the lowest multiple of all the given numbers that is common in all.
Given:
We are given the numbers:
12, 63 and 99
Find:
We need to find their HCF and LCM.
Solution:
HCF of the numbers by prime factorization method:
12, 63 and 99:
Divide all numbers by 3:
4, 21 and 33
We can see that now their is no common factor that can divide thee numbers.
So, HCF = 3.
LCM of the numbers by prime factorization method:
12, 63 and 99:
Divide all numbers by 3:
4, 21 and 33
Now, we have:
4 = 2 × 2
21 = 3 ×7
33 = 3 × 11
LCM = 2 × 2 × 3 × 3 × 3 × 7 × 11
LCM = 8316.
Therefore, we get that the HCF is 3 and the LCM is 8316.
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