GCF and LCM — Drills
GCF and LCM has 5 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 5 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Factor — A number that divides evenly into another.
- Multiple — The result of multiplying by a whole number: 12 is a multiple of 4.
- GCF — Greatest common factor — the largest number dividing both.
- LCM — Least common multiple — the smallest number both divide into.
- Prime factorisation — A number written as a product of primes: 60 = 22 · 3 · 5.
Gcf
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the GCF of 28 and 24.
Worked answer
4
Factors shared by 28 and 24
The greatest is 4
Problem 2
Find the GCF of 36 and 12.
Worked answer
12
Factors shared by 36 and 12
The greatest is 12
Lcm
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the LCM of 7 and 16.
Worked answer
112
GCF is 1
LCM = 7 × 161 = 112
Problem 2
Find the LCM of 11 and 14.
Worked answer
154
GCF is 1
LCM = 11 × 141 = 154
Primefact
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
What is the prime factorisation of 24?
- 23 · 3
- 23 · 32
- 22 · 32
- 22 · 3 · 5
Worked answer
23 · 3
24 = 23 · 3
Problem 2
What is the prime factorisation of 100?
- 23 · 3
- 22 · 3 · 5
- 22 · 52
- 22 · 32
Worked answer
22 · 52
100 = 22 · 52
Word problems
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A florist has 42 roses and 21 tulips and wants identical bunches using every flower. What is the greatest number of bunches?
Worked answer
21
GCF of 42 and 21
= 21 bunches
Problem 2
Two lighthouses flash every 12 and 15 seconds, together right now. After how many seconds do they next flash together?
Worked answer
60
LCM of 12 and 15
= 60 seconds
Product
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Two numbers have GCF 12 and LCM 180. One of them is 60. Find the other.
Worked answer
36
12 × 180 = 2160
2160 ÷ 60 = 36
Problem 2
Two numbers have GCF 6 and LCM 210. One of them is 30. Find the other.
Worked answer
42
6 × 210 = 1260
1260 ÷ 30 = 42