LCM of 3 and 10

LCM of 3 and 10 is the smallest number among all common multiples of 3 and 10. The first few multiples of 3 and 10 are (3, 6, 9, 12, . . . ) and (10, 20, 30, 40, . . . ) respectively. There are 3 commonly used methods to find LCM of 3 and 10 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 3 and 10 is 30.

Explanation:

The LCM of two non-zero integers, x(3) and y(10), is the smallest positive integer m(30) that is divisible by both x(3) and y(10) without any remainder.

The methods to find the LCM of 3 and 10 are explained below.

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

LCM of 3 and 10 by Listing Multiples

To calculate the LCM of 3 and 10 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 3 (3, 6, 9, 12, . . . ) and 10 (10, 20, 30, 40, . . . . )
• Step 2: The common multiples from the multiples of 3 and 10 are 30, 60, . . .
• Step 3: The smallest common multiple of 3 and 10 is 30.

∴ The least common multiple of 3 and 10 = 30.

LCM of 3 and 10 by Division Method

To calculate the LCM of 3 and 10 by the division method, we will divide the numbers(3, 10) by their prime factors (preferably common). The product of these divisors gives the LCM of 3 and 10.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 3 and 10. Write this prime number(2) on the left of the given numbers(3 and 10), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (3, 10) 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 3 and 10 is the product of all prime numbers on the left, i.e. LCM(3, 10) by division method = 2 × 3 × 5 = 30.

LCM of 3 and 10 by Prime Factorization

Prime factorization of 3 and 10 is (3) = 3¹ and (2 × 5) = 2¹ × 5¹ respectively. LCM of 3 and 10 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3¹ × 5¹ = 30.
Hence, the LCM of 3 and 10 by prime factorization is 30.

☛ Also Check:

• LCM of 5 and 13 - 65
• LCM of 15, 30 and 90 - 90
• LCM of 8 and 14 - 56
• LCM of 4, 12, 16 and 24 - 48
• LCM of 96 and 404 - 9696
• LCM of 3 and 12 - 12
• LCM of 20 and 50 - 100

FAQs on LCM of 3 and 10

What is the LCM of 3 and 10?

The LCM of 3 and 10 is 30. To find the LCM of 3 and 10, we need to find the multiples of 3 and 10 (multiples of 3 = 3, 6, 9, 12 . . . . 30; multiples of 10 = 10, 20, 30, 40) and choose the smallest multiple that is exactly divisible by 3 and 10, i.e., 30.

If the LCM of 10 and 3 is 30, Find its GCF.

LCM(10, 3) × GCF(10, 3) = 10 × 3
Since the LCM of 10 and 3 = 30
⇒ 30 × GCF(10, 3) = 30
Therefore, the GCF = 30/30 = 1.

How to Find the LCM of 3 and 10 by Prime Factorization?

To find the LCM of 3 and 10 using prime factorization, we will find the prime factors, (3 = 3) and (10 = 2 × 5). LCM of 3 and 10 is the product of prime factors raised to their respective highest exponent among the numbers 3 and 10.
⇒ LCM of 3, 10 = 2¹ × 3¹ × 5¹ = 30.

What are the Methods to Find LCM of 3 and 10?

The commonly used methods to find the LCM of 3 and 10 are:

• Listing Multiples
• Prime Factorization Method
• Division Method

What is the Least Perfect Square Divisible by 3 and 10?

The least number divisible by 3 and 10 = LCM(3, 10)
LCM of 3 and 10 = 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5]
⇒ Least perfect square divisible by each 3 and 10 = LCM(3, 10) × 2 × 3 × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.