Greatest Common Factor and Least Common Multiple
Math ⇒ Number and Operations
Greatest Common Factor and Least Common Multiple starts at 6 and continues till grade 12.
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See sample questions for grade 12
A factory produces two products, one every 18 minutes and the other every 24 minutes. If both products are started at the same time, after how many minutes will both be produced together again?
A teacher wants to arrange 60 red pens and 84 blue pens in equal groups with no pens left over. What is the greatest number of groups possible?
Explain how the prime factorization of two numbers can be used to find their GCF and LCM.
Explain the difference between the greatest common factor and the least common multiple.
Find the GCF and LCM of 105 and 168.
Find the GCF of 23 × 32 × 5 and 22 × 3 × 7.
A factory produces two products, one every 18 minutes and the other every 24 minutes. If both products are started at the same time, after how many minutes will both be produced together again?
A teacher wants to arrange 60 red pens and 84 blue pens in equal groups with no pens left over. What is the greatest number of groups possible?
Which method is generally more efficient for finding the GCF of two large numbers?
(1) Listing all factors
(2) Prime factorization
(3) Euclidean algorithm
(4) Guess and check
Which of the following is NOT a method to find the LCM of two numbers?
(1) Prime factorization
(2) Listing multiples
(3) Subtracting the numbers repeatedly
(4) Division method
Which of the following is the GCF of 56, 98, and 210?
(1) 7
(2) 14
(3) 28
(4) 42
Which of the following pairs of numbers are coprime?
(1) 14 and 21
(2) 15 and 28
(3) 18 and 27
(4) 24 and 36
Fill in the blank: The GCF of any number and 1 is _______.
Fill in the blank: The LCM of two numbers is always _______ or greater than the larger number.
The GCF of 0 and any nonzero integer is _______.
The GCF of 120 and 45 is _______.
If two numbers are both multiples of 12, is their GCF always 12?
True or False: The LCM of two numbers is always a multiple of their GCF.
True or False: The LCM of two prime numbers is always their product.
True or False: The product of the GCF and LCM of two numbers is equal to the product of the numbers themselves.
