Modular GCD LCM Quiz: Real-Life Math Applications

1) Compute: (34 + 19) mod 8

4

5

1

7

34+19=53;53=8×6+5→remainder=5.

Explanation

34+19=53;53=8×6+5→remainder=5.

Submit

3) Modular addition is both commutative and associative.

True

False

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

Explanation

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

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

(3 + 0) mod 6

24 mod 6

(9 + 3) mod 6

4

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

Explanation

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

Submit

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

Saturday

Sunday

Monday

Tuesday

23mod7=2→Thursday+2=Saturday.

Explanation

23mod7=2→Thursday+2=Saturday.

Submit

7) Find GCD(60, 84).

6

12

24

18

60=2²×3×5;84=2²×3×7→GCD=2²×3=12.

Explanation

60=2²×3×5;84=2²×3×7→GCD=2²×3=12.

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

True

False

a×b=LCM×GCD=72×8=576.

Explanation

a×b=LCM×GCD=72×8=576.

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

8:30 AM

8:45 AM

9:00 AM

9:15 AM

LCM(15,20)=60→9:00.

Explanation

LCM(15,20)=60→9:00.

10) Select all pairs whose LCM is 120.

12 and 30

24 and 40

20 and 30

15 and 40

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

Explanation

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

Submit

11) Simplify: (125 + 75) mod 14

4

8

10

12

125+75=200;200−196=4→200mod14=4.

Explanation

125+75=200;200−196=4→200mod14=4.

Submit

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

True

False

If GCD=1→LCM=a×b.

Explanation

If GCD=1→LCM=a×b.

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

100m

200m

350m

400m

2350÷500=4r350→mod500=350.

Explanation

2350÷500=4r350→mod500=350.

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

0

1

2

5

2+3=5→5mod5=0.

Explanation

2+3=5→5mod5=0.

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

60 days

120 days

240 days

480 days

6=2×3;8=2³;10=2×5→LCM=2³×3×5=120.

Explanation

6=2×3;8=2³;10=2×5→LCM=2³×3×5=120.

Submit

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

True

False

LCM is a multiple of both numbers.

Explanation

LCM is a multiple of both numbers.

19) Compute: (45 + 68) mod 9

0

2

4

5

45+68=113;113−108=5→mod9=5.

Explanation

45+68=113;113−108=5→mod9=5.

20) Select all statements that are always true.

GCD(a,b) divides both a and b

LCM(a,b) divides both a and b

A×b=GCD(a,b)×LCM(a,b)

GCD(a,b)=1 if a,b even

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

Explanation

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

Submit

Modular GCD LCM Quiz: Real-Life Math Applications

1) Compute: (34 + 19) mod 8

2)

What first name or nickname would you like us to use?

2) If x ≡ 6 (mod 7) and y ≡ 5 (mod 7), then x + y ≡ ___ (mod 7).

3) Modular addition is both commutative and associative.

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

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

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

7) Find GCD(60, 84).

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

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

10) Select all pairs whose LCM is 120.

11) Simplify: (125 + 75) mod 14

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

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

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

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

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

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

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

19) Compute: (45 + 68) mod 9

20) Select all statements that are always true.

Modular GCD LCM Quiz: Real-Life Math Applications

1) Compute: (34 + 19) mod 8

2)

What first name or nickname would you like us to use?

2) If x ≡ 6 (mod 7) and y ≡ 5 (mod 7), then x + y ≡ ___ (mod 7).

3) Modular addition is both commutative and associative.

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

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

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

7) Find GCD(60, 84).

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

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

10) Select all pairs whose LCM is 120.

11) Simplify: (125 + 75) mod 14

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

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

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

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

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

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

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

19) Compute: (45 + 68) mod 9

20) Select all statements that are always true.

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