CDS 2026 (I) Elementary Mathematics, question 23

Topic: HCF and LCM

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Q23

The HCF and LCM of two numbers $p$ and $q$ are $44$ and $4620$ respectively. When $p$ is divided by $55$ , the quotient is $4$ and remainder is $0$ . What is the value of $q$ ?

(a) $770$
(b) $924$ Correct answer
(c) $1155$
(d) $2310$

Solution.

Answer: (b) $924$

The division condition gives $p = 55 \times 4 = 220$ .
For two positive integers, $pq = HCF \times LCM$ , so $q = (44 \times 4620)/220 = 924$ .
Check: $220 = 44 \times 5$ and $924 = 44 \times 21$ , with 5 and 21 coprime.