Discrete Mathematics Questions and Answers – Number Theory – Least Common Multiples

This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Number Theory – Least Common Multiples”.

1. A Least Common Multiple of a, b is defined as __________
a) It is the smallest integer divisible by both a and b
b) It is the greatest integer divisible by both a and b
c) It is the sum of the number a and b
d) None of the mentioned
View Answer

Answer: a
Explanation: Definition of LCM(a, b)-smallest multiple of a and b.

2. The LCM of two number 1, b(integer) are _________
a) b + 2
b) 1
c) b
d) None of the mentioned
View Answer

Answer: c
Explanation: Since b is the smallest integer divisible by 1 and b.

3. If a, b are integers such that a > b then lcm(a, b) lies in _________
a) a>lcm(a, b)>b
b) a>b>lcm(a, b)
c) lcm(a, b)>=a>b
d) none of the mentioned
View Answer

Answer: c
Explanation: LCM of number is either equal to the biggest number or greater than all.
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4. LCM of 6, 10 is?
a) 60
b) 30
c) 10
d) 6
View Answer

Answer: b
Explanation: Since 30 is the smallest integer divisible by 6 and 10.

5. The product of two numbers are 12 and their Greatest common divisor is 2 then LCM is?
a) 12
b) 2
c) 6
d) None of the mentioned
View Answer

Answer: c
Explanation: The lcm of two number a and b is given by
lcm(a, b) = ab/(GCD(a, b)).

6. If LCM of two number is 14 and GCD is 1 then the product of two numbers is?
a) 14
b) 15
c) 7
d) 49
View Answer

Answer: a
Explanation: The lcm of two number a and b is given by
lcm(a, b) = ab/(GCD(a, b)), this implies ab = lcm(a, b) * gcd(a, b).

7. If a number is 22 x 31 x 50 and b is 21 x 31 x 51 then lcm of a, b is?
a) 22 x 31 x 51
b) 22 x 32 x 52
c) 23 x 31 x 50
d) 22 x 32 x 50
View Answer

Answer: a
Explanation: Lcm is the product of sets having highest exponent value among a and b.
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8. State whether the given statement is True or False.
LCM (a, b, c, d) = LCM(a,(LCM(b,(LCM(c, d)))).
a) True
b) False
View Answer

Answer: a
Explanation: LCM function can be reursively defined.

9. LCM(a, b) is equals to _________
a) ab/(GCD(a, b))
b) (a+b)/(GCD(a, b))
c) (GCD(a, b))/ab
d) none of the mentioned
View Answer

Answer: a
Explanation: ab = lcm(a, b)*gcd(a, b), which implies
LCM(a,b) = ab/(GCD(a,b)).
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10. The lcm of two prime numbers a and b is _________
a) ab
b) ab
c) a + b
d) 1
View Answer

Answer: b
Explanation: LCM(a, b) = ab/(GCD(a, b)), Since (GCD(a, b)) = 1 therfore LCM(a, b) = ab.

Sanfoundry Global Education & Learning Series – Discrete Mathematics.

To practice all areas of Discrete Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.

If you find a mistake in question / option / answer, kindly take a screenshot and email to [email protected]

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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