LCM of Algebraic Expressions — O/L Mathematics

What must I remember about LCM of Algebraic Expressions?

• The Least Common Multiple (LCM) of algebraic expressions is the simplest polynomial divisible by each given expression without remainder.
• Step 1: Factorise each algebraic expression completely into its prime algebraic factors and numerical prime factors.
• Step 2: Identify each distinct factor occurring across all given expressions.
• Step 3: Take the highest power of each distinct factor and find their product to establish the LCM.
• LCM of monomials: Find LCM of numerical coefficients and multiply by each variable raised to its highest occurring exponent (e.g., LCM of 4x²y and 6xy³ is 12x²y³).

Test yourself (1 minute)

1. HCF vs LCM confusion

   Highest Common Factor (HCF) takes common factors with LOWEST powers; LCM takes ALL factors with HIGHEST powers.

2. Factorise binomials first

   Before finding LCM of (x² - 4) and (x + 2)², factorise them into (x - 2)(x + 2) and (x + 2)²; LCM is (x - 2)(x + 2)².

3. Leave LCM in factored form

   In Paper 1 Part A, it is standard practice to leave the algebraic LCM in factorised form; do not waste time expanding brackets.

Practise LCM of Algebraic Expressions questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 10, Unit 11)

What comes next?

Next in the syllabus

Where does LCM of Algebraic Expressions fit in the syllabus?

Grade 10 · Term 2