This guide explains a topic and a method for reading related news. It does not report a newly announced event. Check the issuing authority for current facts.
01 / UNDERSTANDING
Reading the news
Timetables and repeated service cycles can inspire arithmetic exercises, provided the cycle assumptions are stated. Distinguish an ideal recurring model from an actual operational schedule that may change.
02 / UNDERSTANDING
The concept in context
Prime factorisation makes the distinction explicit. HCF uses shared prime factors with the smallest available powers, whereas LCM uses every needed prime factor with the largest power. For two positive integers, their product equals HCF times LCM, which provides a useful check but should not be applied indiscriminately as a three-number formula.
03 / UNDERSTANDING
A worked learning case
Original educational case. An original supply exercise has 24 pencils and 36 pens to form the greatest number of identical packs with no leftovers. HCF is 12, so twelve packs each contain two pencils and three pens. If instead two reminders repeat every 24 and 36 minutes, their next shared occurrence after starting together is 72 minutes, the LCM.
ORIGINAL EDUCATIONAL PRACTICE
Try it before you check.
Original practice: What are the HCF and LCM of 12 and 18?
Show the answer and reasoning
HCF 6; LCM 36.
Write 12 = 2² × 3 and 18 = 2 × 3². The shared minimum powers give 2 × 3 = 6 for HCF. The maximum powers give 2² × 3² = 36 for LCM. As a check, 12 × 18 and 6 × 36 both equal 216.
Two traps to watch for.
- Choosing LCM for a greatest identical-grouping question.
- Applying the two-number product identity directly to three numbers.
YOUR TOPIC-SPECIFIC LEARNING MAP
Evidence to check
Identify grouping or repeat-cycle language.
Write the prime powers clearly.
Check divisibility of the proposed result.
Explain the idea, apply it to a new situation, then check what changed in your reasoning.
BANKERS TUTORIAL · SOURCE NOTES
Keep the source alongside your notes.
Official links provide subject context and authoritative reference material. This guide’s explanation, scenario and question are original Bankers Tutorial learning content.
- www.ibps.in https://www.ibps.in/
- www.ibps.in https://www.ibps.in/index.php/faq/
For IBPS & RRB preparation, check the current official notice before relying on changing dates, rules or examination requirements.
