AQA · Mathematics · 8300
GCSE Maths: Number: product of primes (LCM/HCF)
Number · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Number: product of primes (LCM/HCF) (Corbettmaths Video 224), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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What does LCM stand for in mathematics?
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Lowest Common Multiple
What does HCF stand for in mathematics?
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Highest Common Factor
Given 60 = 2² × 3 × 5 and 84 = 2² × 3 × 7, what is the HCF of 60 and 84?
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12 (which is 2² × 3, taking the lowest power of each common prime factor)
Given 60 = 2² × 3 × 5 and 84 = 2² × 3 × 7, what is the LCM of 60 and 84?
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420 (which is 2² × 3 × 5 × 7, taking the highest power of each prime factor that appears)
A red light flashes every 28 seconds and a green light flashes every 24 seconds. If they flash together now, after how many seconds will they next flash together?
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168 seconds (the LCM of 28 and 24)
What is the HCF of any two consecutive integers like 20 and 21?
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1 (not 0, as consecutive integers share no common factors other than 1)
Given C = 2⁵ × 3² × 7⁴ and D = 2 × 3² × 5 × 7², what is the HCF of C and D?
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2 × 3² × 7² = 126 (taking minimum powers: 2¹, 3², 7², and excluding 5 which isn't in C)
Given C = 2⁵ × 3² × 7⁴ and D = 2 × 3² × 5 × 7², what is the LCM of C and D?
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2⁵ × 3² × 5 × 7⁴ (taking maximum powers: 2⁵, 3², 5¹, 7⁴)
What is the Highest Common Factor (HCF) of y and 5y?
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y
To make a number a perfect square, what property must all exponents in its prime factorization have?
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All exponents must be even.
To make a number a perfect cube, what property must all exponents in its prime factorization have?
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All exponents must be divisible by 3 (multiples of 3).
If 16200 = 2³ × 3⁴ × 5², what is the smallest whole number to multiply by to make a cube number?
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2² × 3² × 5 = 180. (Each exponent must become divisible by 3: 3→3, 4→6, 2→3)
If 4116 = 2² × 3 × 7³, what is the smallest integer to multiply by to make a square number?
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3 × 7 = 21. (Each exponent must become even: 2→2, 1→2, 3→4)
How do you find the HCF from two numbers written as products of prime factors?
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Take the product of all common prime factors, each raised to the minimum power that appears in either factorization.
How do you find the LCM from two numbers written as products of prime factors?
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Take the product of all prime factors that appear in either number, each raised to the maximum power that appears.
What is the relationship between two numbers A and B, their HCF, and their LCM?
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A × B = HCF(A,B) × LCM(A,B)
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