Multiples of 42

Multiples of 42 are the product of any natural number with 42. That is, we get multiples of 42 when 42 is multiplied by any natural number. Therefore, the list of all multiples of 42 starts with 42 × 1 = 42 and extends up to infinity. There are infinite multiples of 42. The number with which 42 is multiplied to get the multiples of 42 are factors of those multiples. Those numbers which can completely divide 42 are called the factors of 42.

What are the Multiples of 42?

Multiples of a number are obtained by multiplying that number with any natural number. The list of first few multiples of 42 are 42, 84, 126, 168, 210, 252, 294, 336, 378, 420, 462, 504, 546, 588, 630, 672, 714, 756, 798, 840,……. these are the multiples obtained by multiplication of 42 with the first 20 natural numbers. Thus, all those products which appear in the times table of 42 are the multiples of 42.

Factors and Multiples of 42

As multiples of 42 are obtained by multiplying natural numbers with 42, factors of 42 are the numbers that completely divide 42. Factors of a number determine whether the number is a prime number or composite number. If the number has only two factors viz., 1 and itself, the number is a prime number, whereas if it has more than two factors, it is a composite number. Therefore, factors of 42 are 1, 2, 3, 6, 7,14 and 21. Since 42 has more than two factors, then 42 is a composite number.

Difference between Multiples of 42 and Factors of 42

Common Multiples of 42

The common multiples of 42 with any other number is the number of multiples, which are the same in the times table of both the numbers.

For example, common multiples of 42 and 14

The common multiples among the first ten multiples of both the numbers are 42, 84, and 126. There will be infinitely many common multiples of 42 and 14. This is why we always find the lowest common multiple of any given numbers, as it is impossible to find the greatest common multiple of the given numbers.

Lowest Common Multiple of 42

The lowest common multiple of 42 with any other given number is the lowest number which 42 and the given number both can divide.

Let us understand with an example:

The lowest common multiple of 42 and 70

Clearly, the lowest common multiple or LCM of 42 and 70 is 210. That is, 210 is the lowest number which 42 and 70 both can divide.

Video Lesson on Common Multiples

Important Facts on Multiples of 42

• Every multiple of 42 is an even number.
• The lowest multiple of 42 is 42 itself (42 × 1 = 42)
• The greatest multiple of 42 cannot be determined
• The n^th multiple of 42 can be determined by 42 × n
• 42 is a factor of each multiple of 42.
• Each factor of 42 is a factor of multiples of 42.
• All multiples of 42 form a sequence, rather an arithmetic progression in which each term differs by 42.

Related Articles on Multiples of 42

• Factors and Multiples of a number
• Lowest Common Multiple
• Greatest Common Divisor
• Relation between HCF and LCM

Solved Examples on Multiples of 42

Example 1:

List five multiples of 42.

Solution:

We can list any five multiples of 42.

Five multiples of 42 are 42, 84, 126, 168, 210.

Example 2:

Find the 100^th multiple of 42.

Solution:

The 100^th multiple of 42 is 42 ×100 = 4200.

Example 3:

In a matchbox, there are 42 matches. A carton contains 782 matchboxes. How many matches does the carton contain?

Solution:

The carton will contain matches equal to 782nd multiple of 42,

that is, 42 is 42 × 782 = 32,844

Therefore, 32,844 matches are there in the carton.