This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “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

Explanation: Defination 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

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

Explanation: LCM of number is either equal to biggest number or greater than all.

4. LCM of 6, 10 is:

a) 60

b) 30

c) 10

d) 6

View Answer

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

5. The product of two numbers are 12 and there Greatest common divisior is 2 then LCM is:

a) 12

b) 2

c) 6

d) None of the mentioned.

View Answer

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

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 2^{2} x 3^{1} x 5^{0} and b is 2^{1} x 3^{1} x 5^{1} then lcm of a, b is:

a) 2^{2} x 3^{1} x 5^{1}

b) 2^{2} x 3^{2} x 5^{2}

c) 2^{3} x 3^{1} x 5^{0}

d) 2^{2} x 3^{2} x 5^{0}

View Answer

Explanation: Lcm is the product of sets having highest exponent value among a and b.

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

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

Explanation: ab = lcm(a, b)*gcd(a, b), which implies

LCM(a,b) = ab/(GCD(a,b)).

10. The lcm of two prime numbers a and b is:

a) ^{a}⁄_{b}

b) ab

c) a + b

d) 1

View Answer

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.**

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