Question

What are the HCF, LCF, and LCM of 50 and 105?

Answer 1

Hint: To solve this question first we find the prime factor of both the numbers. First, we find the highest common factor, and as we know that lowest common factor is always one and we find the lowest common multiples of both the numbers.

Complete step-by-step answer:
We have given two numbers that are 50 and 105.
First, we find the prime factor of both numbers.
Prime factors of 50 are:
\[50 = 2 \times 5 \times 5\]
The prime factor of 105 are:
\[105 = 3 \times 5 \times 7\]
Now we are going to find highest common factor-
The highest common factor is the factor that is common in both the multiplication:
The highest common factor of 50 and 105 is:
5
The lowest common factor is always 1.
The lowest common multiple is the multiplication of all the prime factors and the common factor is multiplied only once.
The lowest common multiple of 50 and 105 is \[2 \times 3 \times 5 \times 5 \times 7 = 1050\]

Note: To solve this type of question we must know all the basic terms and how we find all the values according to their rule. Students often make mistakes in finding the values and they exchange all the terms. Although this question is very easy. In exams the students are also asked for the definitions and the terms used in these types of questions that are the prime factors and many more. Some of the quantities are fixed like the lowest common factor that is always one not dependent on the number.