LCM and HCF — Study Notes for Bihar TET Paper I
Overview
LCM (Lowest Common Multiple) and HCF (Highest Common Factor) form the backbone of number-system problems in Bihar TET Paper I Mathematics. These concepts test a candidate's understanding of divisibility, factors, and multiples — skills essential for teaching primary-level arithmetic.
In the exam, expect 2–3 direct questions on finding LCM/HCF using various methods, plus application-based word problems involving time intervals, distribution of items, or measurement conversions. Mastery here also supports related topics like fractions, ratio-proportion, and simplification.
For classroom teaching, these concepts help children understand why numbers behave the way they do when grouped, shared, or repeated — making this topic both exam-critical and pedagogically significant.
Key Concepts
- **Factors** are numbers that divide a given number exactly (without remainder). Example: Factors of 12 are 1, 2, 3, 4, 6, 12.
- **Multiples** are products obtained by multiplying a number by natural numbers. Example: Multiples of 4 are 4, 8, 12, 16, 20...
- **HCF (Highest Common Factor)** is the largest number that divides two or more numbers exactly. Also called GCD (Greatest Common Divisor).
- **LCM (Lowest Common Multiple)** is the smallest number that is a multiple of two or more numbers.