GCF and LCM

The GCF of 25 and 30

• 9

• 5

• 12

• 8

What is the GCF of 1283 and 9299

• 2

• 38

• 34

• 1

Lane strikes her drum every 9 seconds and Rory plucks her guitar every 15 seconds. They strike and pluck at the same time at the beginning of the song. After how many seconds will they next strike and pluck together?

• 45 Seconds

• 40 Seconds

• 18 Seconds

• 30 Seconds

David has a length of ribbon which is 180cm long. Kylie’s length of ribbon is 225cm long. They want to cut the longest lengths of ribbon they can from their lengths without wasting any, and in such a way that every piece of ribbon they cut is equal in length. How long will the lengths be?

• 45 cm

• 40 cm

• 180 cm

• 225 cm

Express 960 as the product of prime factors. Use your result to show that 15 is the largest odd factor of 960.

• 2 x 3 × 5 × 6

  6 and 5 are the only even factors so 6×5 is the largest even factor.

• 2 x 13 × 3 × 5

  3 and 5 are the only odd factors so 13×5 is the largest odd factor.

• 2 × 3 × 5

  3 and 5 are the only odd factors so 3×5 is the largest odd factor.

• 26 × 3 × 5

  3 and 5 are the only odd factors so 3×5 is the largest odd factor.

The children at Freeferal Primary School are going on a school trip to Blackpool and every pupil who wants to attend must pay to do so. Mr N Rooly collects £255 from his pupils. Mrs K Ottick collects £136 from her pupils. If the cost is a whole number of pounds, what is the highest it could be?

• LCM = 2040.

  £2040 is the highest cost.

• HCF = 17.

  £17 is the highest cost.

• LCM = 17.

  £17 is the highest cost.

• LCM = 2040.

  £17 is the highest cost.

The highest common factor of two numbers is 32. The lowest common multiple of the two numbers is 640. What could the two numbers be?

• 32 and 128

  or 160 and 640

• 160 and 32

  or 128 and 640

• 640 and 128

  or 32 and 160

• 160 and 128

  or 32 and 640

Cain washes his bedding every 4 weeks. Chas washes her bedding every 5 days. If they both wash

their bedding on April 1st, what is the next date they will both wash their bedding?

• LCM (28, 5) = 285

  They both wash their bedding on the 18th of August.

• LCM (28, 5) = 280

  They both wash their bedding on the 8th of August.

• LCM (28, 5) = 140

  They both wash their bedding on the 18th of August.

• LCM (28, 5) = 528

  They both wash their bedding on the 18th of August.

By expressing it as the product of prime factors, show that 5625 is a square number.

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Use prime factorisation to show that 27 000 is a cube number and find its cube root.

• 27 000 = 2^3 × 3^3 × 7^3 = (2 × 3 × 7)^3 = 30^3

• 27 000 = 2^3 × 3^3 × 5^3 = (2 × 3 × 5)3 = 3^03

• 27 000 = 23 × 33 × 53 = (2 × 3 × 5)3 = 303

• 27 000 = 2^3 × 3^3 × 5^3 = (2 × 3 × 5)^3 = 30^3