The HCF of two numbers, each having three digits, is 17 and their LCM is 714. The sum of the numbers will be:

A) 289 B) 391 C) 221 D) 731

Answer & Solution

Correct Answer: Option C

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
1^st number = 17 × 6 = 102
2^nd number = 17 × 7 = 119
Sum = 102 + 119 = 221

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9 Comments

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Hanjala Hasan 5 years ago

@Naveen_Agrawal
In problem said that, each having three digits.
17*1, 17*2, 17*3 are not 3 digit numbers.

Keerthika Senthil 6 years ago

the sum of hcf and lcm of two numbers is 440. if one of the number is 80 and lcm is 360 more than the hcf, find the other number.

Ashwini Tanwar 6 years ago

Value of x and y can be 3 and 14 also as they are also coprime to each other so answer could be 289 also

BK Biswas 6 years ago

The answer would be 391 and 221. So answer both B and C iare correct.

Naveen Agrawal 6 years ago

ans can be 221 and 391 as well. As 42 = 6*7 or 2*21 or 3*14. so there are three possibilities of x and y.

Mushabbir Rahman 7 years ago

In simple method that's is
714÷17=42
42=7×6
17×7=119
17×6=102
119+102=221

Monica Edward 7 years ago

let the no s be 17a and 17b
a and b are co prime
lcm of the nos is 714
17ab=714
ab=7*6
a or b=7 or 6
first no=17*7=119
second no=17*6=102
sum=102+119=221

Raju Ahmed 8 years ago

17*7=119

Vinay 11 years ago

17*7=119 not 221, please correct it

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The HCF of two numbers each having three digits is 17...

The HCF of two numbers, each having three digits, is 17 and their LCM is 714. The sum of the numbers will be:

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