
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
586.2k+ views
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.
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.
Recently Updated Pages
Master Class 8 Social Science: Engaging Questions & Answers for Success

Master Class 8 English: Engaging Questions & Answers for Success

Class 8 Question and Answer - Your Ultimate Solutions Guide

Master Class 8 Maths: Engaging Questions & Answers for Success

Master Class 8 Science: Engaging Questions & Answers for Success

Master Class 9 General Knowledge: Engaging Questions & Answers for Success

Trending doubts
Full form of STD, ISD and PCO

What are the 12 elements of nature class 8 chemistry CBSE

What is the difference between rai and mustard see class 8 biology CBSE

When people say No pun intended what does that mea class 8 english CBSE

Write a short biography of Dr APJ Abdul Kalam under class 8 english CBSE

Compare the manure and fertilizer in maintaining the class 8 biology CBSE


