the sum of two 3 digits numbers is 684 HCF 57 and LCM is x. then sum of x digits
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Step-by-step explanation:
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The required sum of digit is 24.
Step-by-step explanation:
Consider the provided information.
It is given that the HCF of two numbers = 57
Thus, the numbers are multiples of 57
Let, the numbers be 57x and 57y, where x and y are prime to each other.
It is given that there sum is 684.
57x + 57y = 684
x + y = 12
Required possible pair of values of x and y which are prime to each other are (1, 11) and (5, 7).
For (1, 11) the required pairs of numbers are:
{57 × 1 = 57 and 57 × 11 = 627}
For (5, 7)the required pairs of numbers are:
{57 × 5 = 285 and 57 × 7 = 399}
Since, it is given that the numbers are 3 digit number.
Thus the required numbers are 285 and 399.
The LCM of 285 and 399:
285 = 5 × 57
399 = 7 × 57
LCM of the numbers are 5 × 7 × 57 = 1995
The sum of x digits is: 1+9+9+5=24
Hence, the required sum of digit is 24.
#Learn more
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