HCF & LCM Practice Questions with Detailed Solutions – Level 3

HCF and LCM Level 3 Practice Quiz: Remainders, Bells and Fractions

HCF & LCM Level 3 is a Quant Number System practice set on Aptitude360 that mixes remainder-based divisibility problems, bells and runners meeting together, and the HCF and LCM of fractions and decimals. It also covers number pairs built from a known HCF, sum or product. A step-by-step solution follows every question.

What this HCF and LCM set tests

• Least and greatest numbers that leave equal or unequal remainders with given divisors
• Greatest divisor that leaves the same remainder for a set of numbers
• Bells, alarms and lights ringing or blinking together within a period
• Runners and cyclists meeting at the start or together on a circular track
• HCF and LCM of fractions and decimals, including cutting ropes into equal pieces
• Number pairs from a given HCF with a fixed sum, product, ratio or difference
• Least number to add or subtract so a result becomes divisible or leaves a set remainder

Key HCF and LCM formulas and rules

• For two numbers: \( a\times b=\text{HCF}\times\text{LCM} \)
• HCF of fractions in lowest terms: \( \dfrac{\text{HCF of numerators}}{\text{LCM of denominators}} \)
• LCM of fractions in lowest terms: \( \dfrac{\text{LCM of numerators}}{\text{HCF of denominators}} \)
• Same remainder \( r \) for all divisors: \( N=k\times\text{LCM}+r \)
• Greatest divisor leaving equal remainders: \( \text{HCF}(b-a,\ c-b) \)
• Divisor minus remainder constant at \( d \): \( N=k\times\text{LCM}-d \)

Preparation tips for hard HCF and LCM questions

• Before solving, check whether the gap between each divisor and its remainder is constant; this decides which formula applies.
• Reduce every fraction to its lowest terms, and convert decimal intervals and lengths to whole units, before you take the HCF or LCM.
• For pair questions, write the numbers as the HCF times co-prime multipliers and count only the co-prime pairs.
• On circular tracks, the LCM of lap times gives when everyone is back at the start together; for meetings elsewhere on the track, use relative speed.

Who this HCF and LCM practice suits

Students preparing for CAT, IPMAT, SSC and bank exams who already know the basic methods and want practice on harder, multi-step HCF and LCM problems.