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LCM of 42 and 66

LCM of 42 and 66 is the smallest number among all common multiples of 42 and 66. The first few multiples of 42 and 66 are (42, 84, 126, 168, 210, . . . ) and (66, 132, 198, 264, 330, 396, . . . ) respectively. There are 3 commonly used methods to find LCM of 42 and 66 - by listing multiples, by division method, and by prime factorization.

1.	LCM of 42 and 66
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 42 and 66?

Answer: LCM of 42 and 66 is 462.

Explanation:

The LCM of two non-zero integers, x(42) and y(66), is the smallest positive integer m(462) that is divisible by both x(42) and y(66) without any remainder.

Methods to Find LCM of 42 and 66

Let's look at the different methods for finding the LCM of 42 and 66.

By Listing Multiples
By Division Method
By Prime Factorization Method

LCM of 42 and 66 by Listing Multiples

To calculate the LCM of 42 and 66 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 42 (42, 84, 126, 168, 210, . . . ) and 66 (66, 132, 198, 264, 330, 396, . . . . )
Step 2: The common multiples from the multiples of 42 and 66 are 462, 924, . . .
Step 3: The smallest common multiple of 42 and 66 is 462.

∴ The least common multiple of 42 and 66 = 462.

LCM of 42 and 66 by Division Method

To calculate the LCM of 42 and 66 by the division method, we will divide the numbers(42, 66) by their prime factors (preferably common). The product of these divisors gives the LCM of 42 and 66.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 42 and 66. Write this prime number(2) on the left of the given numbers(42 and 66), separated as per the ladder arrangement.
Step 2: If any of the given numbers (42, 66) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 42 and 66 is the product of all prime numbers on the left, i.e. LCM(42, 66) by division method = 2 × 3 × 7 × 11 = 462.

LCM of 42 and 66 by Prime Factorization

Prime factorization of 42 and 66 is (2 × 3 × 7) = 2¹ × 3¹ × 7¹ and (2 × 3 × 11) = 2¹ × 3¹ × 11¹ respectively. LCM of 42 and 66 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3¹ × 7¹ × 11¹ = 462.
Hence, the LCM of 42 and 66 by prime factorization is 462.

☛ Also Check:

LCM of 42 and 66 Examples

Example 1: Find the smallest number that is divisible by 42 and 66 exactly.

Solution:

The smallest number that is divisible by 42 and 66 exactly is their LCM.
⇒ Multiples of 42 and 66:
- Multiples of 42 = 42, 84, 126, 168, 210, 252, 294, 336, 378, 420, 462, . . . .
- Multiples of 66 = 66, 132, 198, 264, 330, 396, 462, . . . .
Therefore, the LCM of 42 and 66 is 462.
Example 2: The GCD and LCM of two numbers are 6 and 462 respectively. If one number is 66, find the other number.

Solution:

Let the other number be m.
∵ GCD × LCM = 66 × m
⇒ m = (GCD × LCM)/66
⇒ m = (6 × 462)/66
⇒ m = 42
Therefore, the other number is 42.
Example 3: Verify the relationship between GCF and LCM of 42 and 66.

Solution:

The relation between GCF and LCM of 42 and 66 is given as,
LCM(42, 66) × GCF(42, 66) = Product of 42, 66
Prime factorization of 42 and 66 is given as, 42 = (2 × 3 × 7) = 2¹ × 3¹ × 7¹ and 66 = (2 × 3 × 11) = 2¹ × 3¹ × 11¹
LCM(42, 66) = 462
GCF(42, 66) = 6
LHS = LCM(42, 66) × GCF(42, 66) = 462 × 6 = 2772
RHS = Product of 42, 66 = 42 × 66 = 2772
⇒ LHS = RHS = 2772
Hence, verified.

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FAQs on LCM of 42 and 66

What is the LCM of 42 and 66?

The LCM of 42 and 66 is 462. To find the least common multiple (LCM) of 42 and 66, we need to find the multiples of 42 and 66 (multiples of 42 = 42, 84, 126, 168 . . . . 462; multiples of 66 = 66, 132, 198, 264 . . . . 462) and choose the smallest multiple that is exactly divisible by 42 and 66, i.e., 462.

How to Find the LCM of 42 and 66 by Prime Factorization?

To find the LCM of 42 and 66 using prime factorization, we will find the prime factors, (42 = 2 × 3 × 7) and (66 = 2 × 3 × 11). LCM of 42 and 66 is the product of prime factors raised to their respective highest exponent among the numbers 42 and 66.
⇒ LCM of 42, 66 = 2¹ × 3¹ × 7¹ × 11¹ = 462.

What is the Relation Between GCF and LCM of 42, 66?

The following equation can be used to express the relation between GCF and LCM of 42 and 66, i.e. GCF × LCM = 42 × 66.

If the LCM of 66 and 42 is 462, Find its GCF.

LCM(66, 42) × GCF(66, 42) = 66 × 42
Since the LCM of 66 and 42 = 462
⇒ 462 × GCF(66, 42) = 2772
Therefore, the GCF = 2772/462 = 6.

What is the Least Perfect Square Divisible by 42 and 66?

The least number divisible by 42 and 66 = LCM(42, 66)
LCM of 42 and 66 = 2 × 3 × 7 × 11 [Incomplete pair(s): 2, 3, 7, 11]
⇒ Least perfect square divisible by each 42 and 66 = LCM(42, 66) × 2 × 3 × 7 × 11 = 213444 [Square root of 213444 = √213444 = ±462]
Therefore, 213444 is the required number.

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