GCD LCM Word Problems Quiz: Real-Life Applications

  • 8th Grade
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| Questions: 20 | Updated: Dec 16, 2025
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1) Two traffic lights change at intervals of 8 minutes and 12 minutes. If both turn green at 2:00 pm, when will they next turn green together?

Explanation

LCM(8,12)=24 → 2:00+24min=2:24 pm.

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About This Quiz
GCD LCM Word Problems Quiz: Real-life Applications - Quiz

Think you can spot the GCD or LCM behind real-life situations? This quiz turns everyday scenarios into quick number challenges. You’ll use GCD and LCM to solve schedules, shared tasks, repeated patterns, and more. Each problem helps you see how often these concepts appear outside the classroom. Try it out... see moreand see how naturally the answers come together.
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2) The greatest common divisor of 54 and 96 is ____.

Explanation

54=2×3³;96=2⁵×3→GCD=2×3=6.

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3) If LCM(a,b)=84 and GCD(a,b)=7, then a×b=588.

Explanation

a×b=GCD×LCM=7×84=588.

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4) Select all pairs with GCD equal to 5.

Explanation

Each pair’s GCD=5 except 30,75→GCD=15.

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5) A bell rings every 18 seconds and another every 24 seconds. After how many seconds will both ring together again?

Explanation

LCM(18,24)=72s.

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6) A school has 48 red and 60 blue flags. What is the greatest number of groups that can be made?

Explanation

GCD(48,60)=12→12 groups.

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7) LCM(14,18)=____.

Explanation

14=2×7;18=2×3²→LCM=2×3²×7=126.

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8) If GCD(45,18)=9, then 9 divides both 45 and 18.

Explanation

By definition GCD divides both numbers.

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9) Two buses stop every 15 and 20 minutes. If both arrive at 9:00 am, when next together?

Explanation

LCM(15,20)=60→9:00+60min=10:00am.

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10) Select all pairs with LCM=60.

Explanation

All pairs have LCM=60.

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11) Three events repeat every 4,6,9 days. After how many days together again?

Explanation

LCM(4,6,9)=36 days.

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12) Using Euclidean Algorithm, GCD(84,30)=____.

Explanation

84÷30=2r24;30÷24=1r6;24÷6=4r0→GCD=6.

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13) If two numbers are relatively prime, their LCM equals their product.

Explanation

If GCD=1→LCM=a×b.

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14) A machine completes one cycle every 45s and another every 60s. When next together?

Explanation

LCM(45,60)=180s=3min.

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15) Select all statements always true.

Explanation

GCD divides both; LCM is multiple of both; identity holds.

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16) A coach has 36 crackers and 48 cheese cubes. Greatest number of identical packs?

Explanation

GCD(36,48)=12→12 packs.

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17) LCM(24,40,90)=____.

Explanation

LCM uses highest powers→2³×3²×5=360.

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18) If GCD(72,120)=24, then 72÷24 and 120÷24 are relatively prime.

Explanation

72÷24=3;120÷24=5;GCD(3,5)=1.

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19) Two playlists loop every 12 and 18 minutes. After how many minutes start together again?

Explanation

LCM(12,18)=36min.

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20) Select correct value for GCD(90,126).

Explanation

GCD(90,126)=18 (90÷18=5,126÷18=7).

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Two traffic lights change at intervals of 8 minutes and 12 minutes. If...
The greatest common divisor of 54 and 96 is ____.
If LCM(a,b)=84 and GCD(a,b)=7, then a×b=588.
Select all pairs with GCD equal to 5.
A bell rings every 18 seconds and another every 24 seconds. After how...
A school has 48 red and 60 blue flags. What is the greatest number of...
LCM(14,18)=____.
If GCD(45,18)=9, then 9 divides both 45 and 18.
Two buses stop every 15 and 20 minutes. If both arrive at 9:00 am,...
Select all pairs with LCM=60.
Three events repeat every 4,6,9 days. After how many days together...
Using Euclidean Algorithm, GCD(84,30)=____.
If two numbers are relatively prime, their LCM equals their product.
A machine completes one cycle every 45s and another every 60s. When...
Select all statements always true.
A coach has 36 crackers and 48 cheese cubes. Greatest number of...
LCM(24,40,90)=____.
If GCD(72,120)=24, then 72÷24 and 120÷24 are relatively prime.
Two playlists loop every 12 and 18 minutes. After how many minutes...
Select correct value for GCD(90,126).
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