LCM of 12 and 15-How to Find LCM of 12 and 15

LCM of 15 and 20 is 60. LCM is an abbreviation for Least Common Multiple and is the least common multiple of both 15 and 20. Whereas, a few of the multiples are 15, 30, 45, 60, 75, 90, and 105 for 15; 20, 40, 60, 80, 100, and 120 for 20. LCM of 15 and 20 is calculated by division method, prime factorization, and by listing multiple methods.

LCM of 15 and 20

What is the LCM of 15 and 20?

Answer: LCM of 15 and 20 is 60

The smallest positive integer, 60, that can be divided by both 15 and 20 without leaving the remainder is the LCM of two non-zero numbers, 15 and 20. LCM of 15 and 20 is determined via several techniques, which are included below:

What is LCM?

Least Common Multiple of two or more numbers is the smallest positive integer that can be divided by each of the given numbers without leaving any remainders.

LCM of 15 and 20 Calculator

How to Find LCM of 15 and 20?

LCM of 15 and 20 are found using various methods that are:

• LCM of 15 and 20 by Prime Factorization
• LCM of 15 and 20 by Listing Multiple
• LCM of 15 and 20 by Long Division Method

LCM of 15 and 20 by Prime Factorization

LCM of 15 and 20 by the prime factorization methods is found as:

• Prime Factor of 15 = 3¹ × 5¹
• Prime Factor of 20 = 2 × 2 × 5 or 2² × 5¹

LCM of 15 and 20 =  2² × 3¹ × 5¹ = 60

Therefore, LCM of 15 and 20 is 60

LCM of 15 and 20 by Listing Multiple

LCM of 15 and 20, is found by listing the multiple of 15 and 20 and then finding the smallest common multiple by comparing.

• Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, and 150.
• Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180 and 200.

Here, 60 is the first common multiple of both 15 and 20.

Therefore, the LCM of 15 and 20 by listing multiples is 60.

LCM of 15 and 20 by Long Division Method

LCM of 15 and 20 by Long Division Method is found by following the steps added below as:

Step 1: Find the smallest prime number (2) that is a factor of at least one of the numbers. Whereas, 15 and 20 should be divided according to the ladder arrangement.

Step 2: If any of the given numbers (15, 20) are multiples of 2, divide them by 2 and record the quotient below. Reducing any number that is not divisible by the prime number is necessary.

Step 3: Continue this process, until 1 is left in the last row.

Thus, the LCM of 15 and 20 by long division method is 2 × 2 × 3 × 5  = 60.

LCM of 15 and 20 by Long Division Method

LCM and HCF of 15 and 20

Least Common Multiple (LCM) of 15 and 15 is 20 and the Highest Common Factor(HCF) of 15 and 20 is 5. We know that,

LCM × HCF = Product of Two Numbers

Prime factors of 15 and 20

• 15 = 3 × 5
• 20 = 2 × 2 × 5

LCM (15, 20) = 2 × 2 × 3 × 5 = 60

HCF (15, 20) = 5.

15 × 20 = LCM (15, 20) × HCF (15, 20)

300 = 60 × 5

300 = 300

LCM of 15 and 20 Examples

Example 1: Find the smallest number that is divisible by 15 and 20 exactly.

LCM is the smallest number that is exactly divisible by 15 and 20.Multiples of 15 and 20:

• Multiples of 15 = 15, 30, 45, 60, 75, 90, 105.
• Multiples of 20 = 20, 40, 60, 80, 100, 120, 140.

Common multiples in 15 and 20 is 60.

Therefore, the LCM of 15 and 20 is 60.

Example 2: GCD and LCM of two numbers are 5 and 60 respectively. If one number is 15, find the other number.

Solution:

Let the other number be x.

GCD × LCM = 15 × x

⇒ x = (GCD × LCM)/15

⇒ x = (5 × 60)/15

⇒ x = 20

Therefore, the other number is 20.

Practice Problems on LCM of 15 and 20

Problem 1: Calculate the LCM of 15 and 20.

Problem 2: Determine the smallest positive integer that is divisible by both 15 and 20.

Problem 3: If x is the LCM of 15 and 20, what is the value of x?

Problem 4: Find the LCM of 15 and 20 using prime factorization.

FAQs on LCM of 12 and 15

What is Least Common Multiple (LCM) of 15 and 20?

LCM of 15 and 20 is 60.

How do you find LCM of 15 and 20 by Prime Factorization?

Finding LCM of 15 and 20 by Prime Factorization method:

• Prime factors of number 15 = 3¹ × 5¹
• Prime factors of number 20 = 2 × 2 × 5 or 2² × 5¹

LCM =  2² × 3¹ × 5¹ = 60

What is the relation between GCD and LCM of 15 and 20?

Relation between 15 and 20 is, GCD (15, 20) × LCM (15, 20) = 15 × 20.

What are the methods for finding LCM of 15 and 20?

Methods used to find the LCM of 15 and 20 are:

• Prime Factorization Method
• Long Division Method
• Listing Common Factors

If the LCM of 20 and 15 is 60, Find its GCF.

LCM(20, 15) × GCF(20, 15) = 20 × 15

Since the LCM of 20 and 15 = 60

⇒ 60 × GCF(20, 15) = 300

Therefore, the greatest common factor (GCF) = 300/60 = 5.