LCM of 15 and 30

LCM of 15 and 30 is the smallest number among all common multiples of 15 and 30. The first few multiples of 15 and 30 are (15, 30, 45, 60, 75, 90, . . . ) and (30, 60, 90, 120, 150, 180, 210, . . . ) respectively. There are 3 commonly used methods to find LCM of 15 and 30 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 15 and 30 is 30.

Explanation:

The LCM of two non-zero integers, x(15) and y(30), is the smallest positive integer m(30) that is divisible by both x(15) and y(30) without any remainder.

The methods to find the LCM of 15 and 30 are explained below.

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

LCM of 15 and 30 by Prime Factorization

Prime factorization of 15 and 30 is (3 × 5) = 3¹ × 5¹ and (2 × 3 × 5) = 2¹ × 3¹ × 5¹ respectively. LCM of 15 and 30 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3¹ × 5¹ = 30.
Hence, the LCM of 15 and 30 by prime factorization is 30.

LCM of 15 and 30 by Listing Multiples

To calculate the LCM of 15 and 30 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 15 (15, 30, 45, 60, 75, 90, . . . ) and 30 (30, 60, 90, 120, 150, 180, 210, . . . . )
• Step 2: The common multiples from the multiples of 15 and 30 are 30, 60, . . .
• Step 3: The smallest common multiple of 15 and 30 is 30.

∴ The least common multiple of 15 and 30 = 30.

LCM of 15 and 30 by Division Method

To calculate the LCM of 15 and 30 by the division method, we will divide the numbers(15, 30) by their prime factors (preferably common). The product of these divisors gives the LCM of 15 and 30.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 15 and 30. Write this prime number(2) on the left of the given numbers(15 and 30), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (15, 30) 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 15 and 30 is the product of all prime numbers on the left, i.e. LCM(15, 30) by division method = 2 × 3 × 5 = 30.

☛ Also Check:

• LCM of 3 and 12 - 12
• LCM of 3 and 11 - 33
• LCM of 3 and 10 - 30
• LCM of 3 and 1 - 3
• LCM of 2923 and 3239 - 119843
• LCM of 28 and 98 - 196
• LCM of 28 and 70 - 140

FAQs on LCM of 15 and 30

What is the LCM of 15 and 30?

The LCM of 15 and 30 is 30. To find the LCM (least common multiple) of 15 and 30, we need to find the multiples of 15 and 30 (multiples of 15 = 15, 30, 45, 60; multiples of 30 = 30, 60, 90, 120) and choose the smallest multiple that is exactly divisible by 15 and 30, i.e., 30.

If the LCM of 30 and 15 is 30, Find its GCF.

LCM(30, 15) × GCF(30, 15) = 30 × 15
Since the LCM of 30 and 15 = 30
⇒ 30 × GCF(30, 15) = 450
Therefore, the greatest common factor = 450/30 = 15.

What is the Least Perfect Square Divisible by 15 and 30?

The least number divisible by 15 and 30 = LCM(15, 30)
LCM of 15 and 30 = 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5]
⇒ Least perfect square divisible by each 15 and 30 = LCM(15, 30) × 2 × 3 × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.

How to Find the LCM of 15 and 30 by Prime Factorization?

To find the LCM of 15 and 30 using prime factorization, we will find the prime factors, (15 = 3 × 5) and (30 = 2 × 3 × 5). LCM of 15 and 30 is the product of prime factors raised to their respective highest exponent among the numbers 15 and 30.
⇒ LCM of 15, 30 = 2¹ × 3¹ × 5¹ = 30.

What is the Relation Between GCF and LCM of 15, 30?

The following equation can be used to express the relation between GCF and LCM of 15 and 30, i.e. GCF × LCM = 15 × 30.