LCM of 60 and 42

LCM of 60 and 42 is the smallest number among all common multiples of 60 and 42. The first few multiples of 60 and 42 are (60, 120, 180, 240, 300, . . . ) and (42, 84, 126, 168, 210, 252, . . . ) respectively. There are 3 commonly used methods to find LCM of 60 and 42 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 60 and 42 is 420.

Explanation:

The LCM of two non-zero integers, x(60) and y(42), is the smallest positive integer m(420) that is divisible by both x(60) and y(42) without any remainder.

Let's look at the different methods for finding the LCM of 60 and 42.

• By Division Method
• By Prime Factorization Method
• By Listing Multiples

LCM of 60 and 42 by Division Method

To calculate the LCM of 60 and 42 by the division method, we will divide the numbers(60, 42) by their prime factors (preferably common). The product of these divisors gives the LCM of 60 and 42.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 60 and 42. Write this prime number(2) on the left of the given numbers(60 and 42), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (60, 42) 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 60 and 42 is the product of all prime numbers on the left, i.e. LCM(60, 42) by division method = 2 × 2 × 3 × 5 × 7 = 420.

LCM of 60 and 42 by Prime Factorization

Prime factorization of 60 and 42 is (2 × 2 × 3 × 5) = 2² × 3¹ × 5¹ and (2 × 3 × 7) = 2¹ × 3¹ × 7¹ respectively. LCM of 60 and 42 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 5¹ × 7¹ = 420.
Hence, the LCM of 60 and 42 by prime factorization is 420.

LCM of 60 and 42 by Listing Multiples

To calculate the LCM of 60 and 42 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 60 (60, 120, 180, 240, 300, . . . ) and 42 (42, 84, 126, 168, 210, 252, . . . . )
• Step 2: The common multiples from the multiples of 60 and 42 are 420, 840, . . .
• Step 3: The smallest common multiple of 60 and 42 is 420.

∴ The least common multiple of 60 and 42 = 420.

☛ Also Check:

• LCM of 10 and 16 - 80
• LCM of 34 and 51 - 102
• LCM of 3 and 14 - 42
• LCM of 3, 5 and 6 - 30
• LCM of 72 and 96 - 288
• LCM of 4, 8 and 12 - 24
• LCM of 9 and 16 - 144

FAQs on LCM of 60 and 42

What is the LCM of 60 and 42?

The LCM of 60 and 42 is 420. To find the LCM of 60 and 42, we need to find the multiples of 60 and 42 (multiples of 60 = 60, 120, 180, 240 . . . . 420; multiples of 42 = 42, 84, 126, 168 . . . . 420) and choose the smallest multiple that is exactly divisible by 60 and 42, i.e., 420.

How to Find the LCM of 60 and 42 by Prime Factorization?

To find the LCM of 60 and 42 using prime factorization, we will find the prime factors, (60 = 2 × 2 × 3 × 5) and (42 = 2 × 3 × 7). LCM of 60 and 42 is the product of prime factors raised to their respective highest exponent among the numbers 60 and 42.
⇒ LCM of 60, 42 = 2² × 3¹ × 5¹ × 7¹ = 420.

What is the Least Perfect Square Divisible by 60 and 42?

The least number divisible by 60 and 42 = LCM(60, 42)
LCM of 60 and 42 = 2 × 2 × 3 × 5 × 7 [Incomplete pair(s): 3, 5, 7]
⇒ Least perfect square divisible by each 60 and 42 = LCM(60, 42) × 3 × 5 × 7 = 44100 [Square root of 44100 = √44100 = ±210]
Therefore, 44100 is the required number.

If the LCM of 42 and 60 is 420, Find its GCF.

LCM(42, 60) × GCF(42, 60) = 42 × 60
Since the LCM of 42 and 60 = 420
⇒ 420 × GCF(42, 60) = 2520
Therefore, the greatest common factor (GCF) = 2520/420 = 6.

What is the Relation Between GCF and LCM of 60, 42?

The following equation can be used to express the relation between GCF and LCM of 60 and 42, i.e. GCF × LCM = 60 × 42.