Problems on LCM and HCF Part 2
21. 
The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:
 
Answer: Option C
Explanation:
Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm.

22. 
Three numbers which are coprime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is:
 
Answer: Option C
Explanation:
Since the numbers are coprime, they contain only 1 as the common factor.
Also, the given two products have the middle number in common.
So, middle number = H.C.F. of 551 and 1073 = 29;
Required sum = (19 + 29 + 37) = 85.

23. 
Find the highest common factor of 36 and 84.
 
Answer: Option C
Explanation:
36 = 2^{2} x 3^{2}
84 = 2^{2} x 3 x 7
H.C.F. = 2^{2} x 3 = 12.

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