Nalanda College, Colombo 10 Grade 11 Maths Worksheet: 7 Algebraic Fractions

LCM of three algebraic terms

Answer: 10a²b²

💡 What it's asking: The LCM (least common multiple) is the smallest expression that every term divides into. Deal with the numbers and the letters separately.

1. 1Numbers first: the smallest number that 5, 10 and 2 all divide into is 10.
2. 2Letter a: the highest power that appears is a², so take a².
3. 3Letter b: the highest power that appears is b², so take b².
4. 4Put them together: LCM = 10a²b².

✅ Divide 10a²b² by each term; you get whole answers 2ab, b and 5a, so every term fits into it.

LCM of two linear expressions

Answer: 2(3a + b)(a − 2)

💡 What it's asking: To find the LCM of algebraic expressions, first break each one into factors. Then take every different factor, using each the most times it appears.

1. 13a + b has no common factor, so leave it as it is.
2. 2Take out the common factor 2: 2a − 4 = 2(a − 2).
3. 3The factors 2, (3a + b) and (a − 2) are all different.
4. 4Multiply each one once: LCM = 2(3a + b)(a − 2).

✅ 2(3a + b)(a − 2) ÷ (3a + b) = 2(a − 2) and ÷ 2(a − 2) = (3a + b): both divide exactly.

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