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: Option C
Solution(By Examveda Team)
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 = 221This Question Belongs to Arithmetic Ability >> Number System
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Comments ( 9 )
Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
@Naveen_Agrawal
In problem said that, each having three digits.
17*1, 17*2, 17*3 are not 3 digit numbers.
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.
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
The answer would be 391 and 221. So answer both B and C iare correct.
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.
In simple method that's is
714÷17=42
42=7×6
17×7=119
17×6=102
119+102=221
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
17*7=119
17*7=119 not 221, please correct it