Modular GCD LCM Quiz: Real-Life Math Applications

  • 8th Grade
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Quizzes Created: 7682 | Total Attempts: 9,547,133
| Questions: 20 | Updated: Dec 16, 2025
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1) Compute: (34 + 19) mod 8

Explanation

34+19=53;53=8×6+5→remainder=5.

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About This Quiz
Modular GCD LCM Quiz: Real-life Math Applications - Quiz

What happens when modular arithmetic meets GCD and LCM? This quiz blends all three ideas into simple, practical questions. You’ll compare numbers, track remainders, break down factors, and see how these concepts support each other. It’s a smooth way to understand how different math tools work together. Jump in and... see moreexplore the connections.
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2) If x ≡ 6 (mod 7) and y ≡ 5 (mod 7), then x + y ≡ ___ (mod 7).

Explanation

6+5=11;11 mod7=4.

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3) Modular addition is both commutative and associative.

Explanation

(a+b)modn=(b+a)modn; associative too.

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4) Select all expressions equivalent to (15 + 9) mod 6.

Explanation

24mod6=0;(9+3)mod6=0.

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5) If today is Thursday, what day will it be in 23 days?

Explanation

23mod7=2→Thursday+2=Saturday.

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6) A digital clock shows 9:00. After 26 hours, it will show ___ o’clock.

Explanation

26mod12=2→9+2=11.

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7) Find GCD(60, 84).

Explanation

60=2²×3×5;84=2²×3×7→GCD=2²×3=12.

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8) If LCM(a, b) = 72 and GCD(a, b) = 8, then a × b = 576.

Explanation

a×b=LCM×GCD=72×8=576.

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9) Two trains arrive every 15 and 20 minutes. If both at 8:00, next together?

Explanation

LCM(15,20)=60→9:00.

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10) Select all pairs whose LCM is 120.

Explanation

24=2³×3,40=2³×5→120;15=3×5,40=2³×5→120.

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11) Simplify: (125 + 75) mod 14

Explanation

125+75=200;200−196=4→200mod14=4.

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12) The least common multiple of 9, 12, and 18 is ____.

Explanation

9=3²,12=2²×3,18=2×3²→LCM=2²×3²=36.

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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 runner circles a 500m track. After running 2,350m, how far into next lap?

Explanation

2350÷500=4r350→mod500=350.

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15) Select all correct results of (a + b) mod 5 when a ≡ 2 and b ≡ 3.

Explanation

2+3=5→5mod5=0.

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16) Three events occur every 6, 8, and 10 days. When next coincide?

Explanation

6=2×3;8=2³;10=2×5→LCM=2³×3×5=120.

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17) If GCD(108,72)=36, then 108÷36 and 72÷36 are ___ and ___, which are relatively prime.

Explanation

108=36×3;72=36×2;GCD(3,2)=1.

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18) LCM(a, b) is always divisible by both a and b.

Explanation

LCM is a multiple of both numbers.

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19) Compute: (45 + 68) mod 9

Explanation

45+68=113;113−108=5→mod9=5.

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20) Select all statements that are always true.

Explanation

LCM is multiple not divisor; even numbers have GCD≥2.

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Compute: (34 + 19) mod 8
If x ≡ 6 (mod 7) and y ≡ 5 (mod 7), then x + y ≡ ___ (mod 7).
Modular addition is both commutative and associative.
Select all expressions equivalent to (15 + 9) mod 6.
If today is Thursday, what day will it be in 23 days?
A digital clock shows 9:00. After 26 hours, it will show ___...
Find GCD(60, 84).
If LCM(a, b) = 72 and GCD(a, b) = 8, then a × b = 576.
Two trains arrive every 15 and 20 minutes. If both at 8:00, next...
Select all pairs whose LCM is 120.
Simplify: (125 + 75) mod 14
The least common multiple of 9, 12, and 18 is ____.
If two numbers are relatively prime, their LCM equals their product.
A runner circles a 500m track. After running 2,350m, how far into next...
Select all correct results of (a + b) mod 5 when a ≡ 2 and b ≡ 3.
Three events occur every 6, 8, and 10 days. When next coincide?
If GCD(108,72)=36, then 108÷36 and 72÷36 are ___ and ___, which are...
LCM(a, b) is always divisible by both a and b.
Compute: (45 + 68) mod 9
Select all statements that are always true.
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