Maths question from Social Forest Worker exam, 2026 by JKSSB
Identify the single correct statement regarding the properties of HCF and LCM:
Last updated Jul 21, 2026
Correct Answer:
Option D —
All of the above statements are correct
Statement A is correct:
If the Highest Common Factor is 13, the two numbers can be written as 13 multiplied by a and 13 multiplied by b, where a and b share no common factors. Multiplying these together gives 169 multiplied by a and b, which equals 2028. Dividing 2028 by 169 gives a multiplied by b equal to 12. The only pair of factors of 12 with no common factors are (1, 12) and (3, 4). This gives exactly two valid pairs of numbers: (13, 156) and (39, 52).
Statement B is correct:
It is a fundamental mathematical rule that the Highest Common Factor of any set of numbers always divides their Lowest Common Multiple completely without leaving a remainder.
Statement C is correct:
Since the Highest Common Factor must divide the Lowest Common Multiple, and 8 does not divide 60 evenly (60 divided by 8 leaves a remainder of 4), 60 can never be the Lowest Common Multiple for two numbers whose Highest Common Factor is 8.
Since statements A, B, and C are all true, Option D is the single correct answer.
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
