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Three numbers are in ratio 1:2:3 and their HCF is 12, the numbers are?
  • a)
    4,8,12
  • b)
    5,10,15
  • c)
    10,20,30
  • d)
    12,24,36
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Three numbers are in ratio 1:2:3 and their HCF is 12, the numbers are?...
Let the numbers be x, 2x and 3x. 
The HCF in x, 2x and 3x is x because 1, 2, 3 are prime.
Hence,
x = 12; then the other numbers are 24 and 36.

So, the numbers are: 12, 24 and 36.
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Most Upvoted Answer
Three numbers are in ratio 1:2:3 and their HCF is 12, the numbers are?...
Since the highest common factor is 12 which should be common in every no and these are divided into 1:2:3 .let's assume them x,2x,3xand if 12 is common then the no should be 12,2*12,3*12 that is 12,24,36
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Community Answer
Three numbers are in ratio 1:2:3 and their HCF is 12, the numbers are?...
To find the three numbers in the ratio 1:2:3 with a highest common factor (HCF) of 12, we can follow these steps:

Step 1: Understanding the ratio
The ratio given is 1:2:3. This means that the three numbers can be represented as x, 2x, and 3x, where x is a common factor.

Step 2: Finding the HCF
The highest common factor (HCF) of three numbers is the largest number that divides all three numbers evenly. Given that the HCF is 12, we can conclude that 12 is a common factor of all three numbers.

Step 3: Expressing the numbers
Since the HCF is 12, we can express the three numbers as 12a, 12b, and 12c, where a, b, and c are co-prime numbers.

Step 4: Applying the ratio
According to the given ratio, we have:
12a : 12b : 12c = 1 : 2 : 3

Step 5: Simplifying the ratio
Dividing all terms by 12, we get:
a : b : c = 1/12 : 2/12 : 3/12
Simplifying further, we have:
a : b : c = 1/12 : 1/6 : 1/4

Step 6: Finding the values
Since a, b, and c are co-prime numbers, the simplified ratio implies that a = 1/12, b = 1/6, and c = 1/4.

Step 7: Multiplying by 12
To obtain whole numbers, we need to multiply each term by 12.
a = 1/12 * 12 = 1
b = 1/6 * 12 = 2
c = 1/4 * 12 = 3

Step 8: Determining the numbers
Therefore, the three numbers that satisfy the given conditions are 12a, 12b, and 12c, which are:
12 * 1 = 12
12 * 2 = 24
12 * 3 = 36

Hence, the correct answer is option D: 12, 24, and 36.
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Three numbers are in ratio 1:2:3 and their HCF is 12, the numbers are?a)4,8,12b)5,10,15c)10,20,30d)12,24,36Correct answer is option 'D'. Can you explain this answer?
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