Lakshya Education MCQs

Question: ___ is a factor of every number.
Options:

: One is the common factor for all the numbers. Each number is divisible by one and the "number itself". For example, 3 is divisible by both 1 and 3.

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Question 1. In which of the following cases, is the first number a factor of the second number?
  1.    4, 38
  2.    6, 52
  3.    8, 96
  4.    5, 33
Answer: Option C
: C

When 38 is divided by 4, the remainder is 2. So, 4 is not a factor of 38.
When 52 is divided by 6, the remainder is 4. So, 6 is not a factor of 52.
When 33 is divided by 5, the remainder is 3. So, 5 is not a factor of 33.
When 96 is divided by 8 the remainder is 0. So, 8 is a factor of 96.
Question 2. The ___ of two or more numbers is the least number which is exactly divisible by those numbers.

: The LCM of two or more numbers is the least number whichis exactly divisible by those numbers. Example: LCM of 4 and 6 is 12. So, 12 is the least number which is exactly divisible by 4 and 6.
Question 3. The largest 2-digit prime number is ___

: Prime numbers are numbers which are divisible by1 and the "number itself", So, 3 is a prime number as it is divisible by only 1 and 3. 99 is not a prime number as it is divisible by 1, 9, 11, 99. 98 is also not a prime number as it is divisible by 1, 2, 7, 49, 98. The largest 2-digit prime number is 97, as it is divisible only by 1 and 97.
Question 4. The smallest number that is divisible by 2,4,6 is____
  1.    8
  2.    12
  3.    9
  4.    36
Answer: Option B
: B

The smallest number divisible by any 2 or more numbers istheir least common multiple (LCM).
The multiples of 2 : 2 , 4 , 6 , 8 , 10 , 12 , 14 .....
The multiples of 4: 4 , 8 , 12 , 16 , 20 ......
The multiples of 6: 6 , 12 , 18 , 24 .........
As you can see, 12 is the smallest multiple that is commom for all 3 numbers.
So, the LCM of 2, 4, 6 = 12
Question 5. The product of two numbers is 228. If their HCF is 12, then what will be their LCM?
  1.    20
  2.    1
  3.    19
  4.    0
Answer: Option C
: C

HCF of two numbers × LCM of two numbers = Product of the two numbers
12×LCM=228
LCM =22812=19
Question 6. Which of the following is a factor pair of 26?
  1.    2 and 13
  2.    1 and 13
  3.    3 and 12
  4.    4 and 6
Answer: Option A
: A

2 and 13 form a factor pair of 26 as 2×13=26.

1 and 13 form a factor pair of 13 as 1×13=13.

3 and 12 form a factor pair of 36 as 3×12=36.

4 and 6 form a factor pair of 24 as 4×6=24.

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