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1. The HCF of two numbers, each having three digits, is 17 and their LCM is 714. The sum of the numbers will be:
LCM = 17xy
Now, 17xy = 714
Or, xy = 42 = 6 × 7
→x = 6 and y = 7
Or, x = 7 and y = 6
1st number = 17 × 6 = 102
2nd number = 17 × 7 = 119
Sum = 102 + 119 = 221
Solution:
Let the numbers be 17x and 17y where x and y are co-prime.LCM = 17xy
Now, 17xy = 714
Or, xy = 42 = 6 × 7
→x = 6 and y = 7
Or, x = 7 and y = 6
1st number = 17 × 6 = 102
2nd number = 17 × 7 = 119
Sum = 102 + 119 = 221