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LCM of 3 and 5

LCM of 3 and 5 is the smallest number among all common multiples of 3 and 5. The first few multiples of 3 and 5 are (3, 6, 9, 12, 15, 18, 21, . . . ) and (5, 10, 15, 20, 25, 30, 35, . . . ) respectively. There are 3 commonly used methods to find LCM of 3 and 5 - by listing multiples, by prime factorization, and by division method.

1.	LCM of 3 and 5
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 3 and 5?

Answer: LCM of 3 and 5 is 15.

Explanation:

The LCM of two non-zero integers, x(3) and y(5), is the smallest positive integer m(15) that is divisible by both x(3) and y(5) without any remainder.

Methods to Find LCM of 3 and 5

Let's look at the different methods for finding the LCM of 3 and 5.

By Division Method
By Listing Multiples
By Prime Factorization Method

LCM of 3 and 5 by Division Method

To calculate the LCM of 3 and 5 by the division method, we will divide the numbers(3, 5) by their prime factors (preferably common). The product of these divisors gives the LCM of 3 and 5.

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

LCM of 3 and 5 by Listing Multiples

To calculate the LCM of 3 and 5 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, 15, 18, 21, . . . ) and 5 (5, 10, 15, 20, 25, 30, 35, . . . . )
Step 2: The common multiples from the multiples of 3 and 5 are 15, 30, . . .
Step 3: The smallest common multiple of 3 and 5 is 15.

∴ The least common multiple of 3 and 5 = 15.

LCM of 3 and 5 by Prime Factorization

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

☛ Also Check:

LCM of 3 and 5 Examples

Example 1: The product of two numbers is 15. If their GCD is 1, what is their LCM?

Solution:

Given: GCD = 1
product of numbers = 15
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 15/1
Therefore, the LCM is 15.
The probable combination for the given case is LCM(3, 5) = 15.
Example 2: Verify the relationship between GCF and LCM of 3 and 5.

Solution:

The relation between GCF and LCM of 3 and 5 is given as,
LCM(3, 5) × GCF(3, 5) = Product of 3, 5
Prime factorization of 3 and 5 is given as, 3 = (3) = 3¹ and 5 = (5) = 5¹
LCM(3, 5) = 15
GCF(3, 5) = 1
LHS = LCM(3, 5) × GCF(3, 5) = 15 × 1 = 15
RHS = Product of 3, 5 = 3 × 5 = 15
⇒ LHS = RHS = 15
Hence, verified.
Example 3: The GCD and LCM of two numbers are 1 and 15 respectively. If one number is 5, find the other number.

Solution:

Let the other number be z.
∵ GCD × LCM = 5 × z
⇒ z = (GCD × LCM)/5
⇒ z = (1 × 15)/5
⇒ z = 3
Therefore, the other number is 3.

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FAQs on LCM of 3 and 5

What is the LCM of 3 and 5?

The LCM of 3 and 5 is 15. To find the least common multiple of 3 and 5, we need to find the multiples of 3 and 5 (multiples of 3 = 3, 6, 9, 12 . . . . 15; multiples of 5 = 5, 10, 15, 20) and choose the smallest multiple that is exactly divisible by 3 and 5, i.e., 15.

What is the Relation Between GCF and LCM of 3, 5?

The following equation can be used to express the relation between GCF and LCM of 3 and 5, i.e. GCF × LCM = 3 × 5.

What is the Least Perfect Square Divisible by 3 and 5?

The least number divisible by 3 and 5 = LCM(3, 5)
LCM of 3 and 5 = 3 × 5 [Incomplete pair(s): 3, 5]
⇒ Least perfect square divisible by each 3 and 5 = LCM(3, 5) × 3 × 5 = 225 [Square root of 225 = √225 = ±15]
Therefore, 225 is the required number.

If the LCM of 5 and 3 is 15, Find its GCF.

LCM(5, 3) × GCF(5, 3) = 5 × 3
Since the LCM of 5 and 3 = 15
⇒ 15 × GCF(5, 3) = 15
Therefore, the greatest common factor = 15/15 = 1.

Which of the following is the LCM of 3 and 5? 36, 21, 28, 15

The value of LCM of 3, 5 is the smallest common multiple of 3 and 5. The number satisfying the given condition is 15.

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