250+ TOP MCQs on Number Theory – Least Common Multiples

Discrete Mathematics Multiple Choice Questions 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

Answer: a
Clarification: 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

Answer: c
Clarification: 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

Answer: c
Clarification: LCM of number is either equal to the biggest number or greater than all.

4. LCM of 6, 10 is?
a) 60
b) 30
c) 10
d) 6

Answer: b
Clarification: 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

Answer: c
Clarification: 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

Answer: a
Clarification: 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

Answer: a
Clarification: 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

Answer: a
Clarification: 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

Answer: a
Clarification: 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

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