Topic Details (Notes format)

How to Find the Least Common Multiple (LCM)

Subject: Mathematics

Book: Maths Mastery

The LCM of two integers is the smallest positive integer that is a multiple of both. For instance, the LCM of 6 and 8 is 24. One method is to list multiples until a common one appears: multiples of 6 are 6, 12, 18, 24, 30..., and multiples of 8 are 8, 16, 24, 32.... 24 is the first match. Alternatively, use the relationship LCM(a, b) × GCD(a, b) = a × b. The LCM is extremely useful for adding fractions with different denominators, coordinating schedules, and dealing with cyclical events. Learning to compute it quickly helps streamline many arithmetic operations and problem-solving scenarios.

Practice Questions

If x^3 - 3x^2 + 4 = 0, what is one root of the equation?

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What is the greatest common divisor (GCD) of 36 and 48?

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If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

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If a = 4 and b = 5, what is the value of (a+b)^2?

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The probability of rolling a sum of 7 with two dice is:

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The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

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A number is increased by 20% and then decreased by 20%. What is the net change?

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What is the sum of the first 50 positive integers?

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If 5x - 2 = 13, what is the value of x?

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If the sum of three consecutive integers is 72, what are the integers?

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