
The ratio of two numbers is 2:3. If their LCM is 150, find the numbers.
(A) 30, 45
(B) 48, 72
(C) 50, 75
(D) 26, 39
Answer
515.1k+ views
Hint:
LCM stands for least common multiple or lowest common multiple. LCM 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. In simple words it is the smallest number that they have in common as a multiple.
Complete step by step solution:
Here the ratio of the two numbers is given as 2:3.
The two numbers can be expressed as 2x and 3x, where x is an integer.
Since 150 is the LCM of 2x and 3x, it is a common multiple of the two numbers, so x must divide 150,
Putting the value of x in the two numbers, we get, and .
Therefore, the two numbers are 50 and 75. Thus .
The correct option is (C).
Note:
For the lowest common multiple to be between 2x and 3x, there must be one 2, one 3 and two 5’s between them. This is satisfied when x is 25. If we use prime factorisation method then:
Prime factorization of 50 is: 2X5X5
Prime factorization of 75 is: 3X5X5
Eliminating duplicates factors and multiplying the remaining we get 150. Thus, verifying our answer above. These questions usually pop up in Olympiads and other exams, to solve such questions, try to learn how to find LCM and HCF effectively. Also memorise the relation between LCM and HCF.
LCM stands for least common multiple or lowest common multiple. LCM 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. In simple words it is the smallest number that they have in common as a multiple.
Complete step by step solution:
Here the ratio of the two numbers is given as 2:3.
The two numbers can be expressed as 2x and 3x, where x is an integer.
Since 150 is the LCM of 2x and 3x, it is a common multiple of the two numbers, so x must divide 150,
Putting the value of x in the two numbers, we get,
Therefore, the two numbers are 50 and 75. Thus
The correct option is (C).
Note:
For the lowest common multiple to be between 2x and 3x, there must be one 2, one 3 and two 5’s between them. This is satisfied when x is 25. If we use prime factorisation method then:
Prime factorization of 50 is: 2X5X5
Prime factorization of 75 is: 3X5X5
Eliminating duplicates factors and multiplying the remaining we get 150. Thus, verifying our answer above. These questions usually pop up in Olympiads and other exams, to solve such questions, try to learn how to find LCM and HCF effectively. Also memorise the relation between LCM and HCF.
Recently Updated Pages
Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Social Science: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Chemistry: Engaging Questions & Answers for Success

Trending doubts
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

How many ounces are in 500 mL class 8 maths CBSE

Name the states through which the Tropic of Cancer class 8 social science CBSE

How many ten lakhs are in one crore-class-8-maths-CBSE

Is the past tense for sink sank or sunk class 8 english CBSE

List some examples of Rabi and Kharif crops class 8 biology CBSE
