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Write any three numbers of two digits. Find the L.C.M and H.C.F for the above numbers by the “Prime Factorization method.”

Answer
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Hint: Prime Factorization method:
The method of prime factorization is used to “break down” or express a given number as a product of prime numbers. More so, if a prime number occurs more than once in the factorization, it is usually expressed in exponential form to make it look more compact.
First we need to write any three numbers then need to express them as a product of prime numbers.
For L.C.M of these three numbers we first need to find out the common prime numbers from the splitted numbers and then multiply them with the numbers left after discarding the common numbers from the splitted numbers.
For H.C.F of the three numbers we just need to multiply the common numbers from the splitted numbers (which are present in three of them).

Complete step-by-step answer:
First we need to write any three two digit numbers, then find out the L.C.M and H.C.F for the above numbers by the “Prime Factorization method.”
Let us take the number\[25,{\text{ }}30,{\text{ }}60\].
The numbers can be written as
\[25 = 1 \times 5 \times 5\]
\[30 = 1 \times 2 \times 3 \times 5\]
\[60 = 1 \times 2 \times 2 \times 3 \times 5\]
= \[1 \times {2^2} \times 3 \times 5\]
The L.C.M for the above numbers by the “Prime Factorization method” is \[1 \times 5 \times 5 \times {2^2} \times 3 = 300\]

The H.C.F for the above numbers by the “Prime Factorization method” is \[5\].

Note: L.C.M:
In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b.
H.C.F:
The greatest number which divides each of the two or more numbers is called HCF or Highest Common Factor. It is also called the Greatest Common Measure (GCM) and Greatest Common Divisor (GCD).
HCF and LCM are two different methods, where LCM or Least Common Multiple is used to find the smallest common multiple of any two or more numbers and HCF or Highest Common Factor is the greatest number which divides each of the two or more numbers.
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