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Three numbers are in the ratio of 3: 4: 5 and their L.C.M. is 2400. Their H.C.F. is :
- a)40
- b)80
- c)120
- d)200
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Three numbers are in the ratio of 3: 4: 5 and their L.C.M. is 2400. Th...
Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x.
So, 60x = 2400 or × = 40.
The numbers are (3 × 40), (4 × 40) and (5 × 40).
Hence, required H.C.F. = 40.
Then, their L.C.M. = 60x.
So, 60x = 2400 or × = 40.
The numbers are (3 × 40), (4 × 40) and (5 × 40).
Hence, required H.C.F. = 40.
Most Upvoted Answer
Three numbers are in the ratio of 3: 4: 5 and their L.C.M. is 2400. Th...
Given:
Three numbers are in the ratio of 3:4:5.
L.C.M. of the numbers is 2400.
To find:
The H.C.F. (Highest Common Factor) of the three numbers.
Solution:
Let the three numbers be 3x, 4x, and 5x, where x is a common factor.
Step 1: Find the value of x:
To find the value of x, we need to find the L.C.M. of the given ratio, which is 3:4:5.
The L.C.M. of 3, 4, and 5 is 60.
So, if we multiply the given ratio by 60, we get the numbers as 180, 240, and 300.
Step 2: Find the H.C.F.:
To find the H.C.F., we need to find the common factors of the numbers 180, 240, and 300.
The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240.
The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.
The common factors of 180, 240, and 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
The highest common factor among these numbers is 60.
Step 3: Find the H.C.F. of the original numbers:
Since we multiplied the original ratio by 60, the H.C.F. of the original numbers will also be multiplied by 60.
Therefore, the H.C.F. of the original numbers is 60 x 40 = 2400.
Hence, the correct answer is option (A) 40.
Three numbers are in the ratio of 3:4:5.
L.C.M. of the numbers is 2400.
To find:
The H.C.F. (Highest Common Factor) of the three numbers.
Solution:
Let the three numbers be 3x, 4x, and 5x, where x is a common factor.
Step 1: Find the value of x:
To find the value of x, we need to find the L.C.M. of the given ratio, which is 3:4:5.
The L.C.M. of 3, 4, and 5 is 60.
So, if we multiply the given ratio by 60, we get the numbers as 180, 240, and 300.
Step 2: Find the H.C.F.:
To find the H.C.F., we need to find the common factors of the numbers 180, 240, and 300.
The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
The factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240.
The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.
The common factors of 180, 240, and 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
The highest common factor among these numbers is 60.
Step 3: Find the H.C.F. of the original numbers:
Since we multiplied the original ratio by 60, the H.C.F. of the original numbers will also be multiplied by 60.
Therefore, the H.C.F. of the original numbers is 60 x 40 = 2400.
Hence, the correct answer is option (A) 40.
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Three numbers are in the ratio of 3: 4: 5 and their L.C.M. is 2400. Their H.C.F. is :a)40b)80c)120d)200Correct answer is option 'A'. Can you explain this answer? for Class 5 2025 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about Three numbers are in the ratio of 3: 4: 5 and their L.C.M. is 2400. Their H.C.F. is :a)40b)80c)120d)200Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 5 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three numbers are in the ratio of 3: 4: 5 and their L.C.M. is 2400. Their H.C.F. is :a)40b)80c)120d)200Correct answer is option 'A'. Can you explain this answer?.
Three numbers are in the ratio of 3: 4: 5 and their L.C.M. is 2400. Their H.C.F. is :a)40b)80c)120d)200Correct answer is option 'A'. Can you explain this answer? for Class 5 2025 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about Three numbers are in the ratio of 3: 4: 5 and their L.C.M. is 2400. Their H.C.F. is :a)40b)80c)120d)200Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 5 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three numbers are in the ratio of 3: 4: 5 and their L.C.M. is 2400. Their H.C.F. is :a)40b)80c)120d)200Correct answer is option 'A'. Can you explain this answer?.
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Three numbers are in the ratio of 3: 4: 5 and their L.C.M. is 2400. Their H.C.F. is :a)40b)80c)120d)200Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Three numbers are in the ratio of 3: 4: 5 and their L.C.M. is 2400. Their H.C.F. is :a)40b)80c)120d)200Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Three numbers are in the ratio of 3: 4: 5 and their L.C.M. is 2400. Their H.C.F. is :a)40b)80c)120d)200Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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