Question

find two numbers each of 3 digits, such that their GCD is 7 and their LCM is 3059

Answer 1

The three digit numbers are 133 and 161.

1. Given the LCM and GCD of numbers is 3059 and 7 respectively.
2. Let us assume the numbers to be x and y.
3. Therefore, x=7a and y =7b (as GCD is 7 both the numbers are multiples of 7)
4. now LCM using the numbers will be LCM = product of both the numbers / GCD of the number = $\frac{7a * 7b}{7}$ = 7ab
5. now LCM = 3059 that is 7ab = 3059

ab=437

• Now we find the factors of 437 and we get the factors as 1,19,23,437
• now the pairs that form 437 are (1,437) (19,23)
• These pairs are the values of (a,b)
• Now we substitute this value in x=7a and y=7b to obtain original numbers
• We get one number as 133 and second as 161 which are the 3 digit numbers.