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LCM of 10 and 60

LCM of 10 and 60 is the smallest number among all common multiples of 10 and 60. The first few multiples of 10 and 60 are (10, 20, 30, 40, 50, . . . ) and (60, 120, 180, 240, . . . ) respectively. There are 3 commonly used methods to find LCM of 10 and 60 - by listing multiples, by division method, and by prime factorization.

1.	LCM of 10 and 60
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 10 and 60?

Answer: LCM of 10 and 60 is 60.

Explanation:

The LCM of two non-zero integers, x(10) and y(60), is the smallest positive integer m(60) that is divisible by both x(10) and y(60) without any remainder.

Methods to Find LCM of 10 and 60

The methods to find the LCM of 10 and 60 are explained below.

By Prime Factorization Method
By Division Method
By Listing Multiples

LCM of 10 and 60 by Prime Factorization

Prime factorization of 10 and 60 is (2 × 5) = 2¹ × 5¹ and (2 × 2 × 3 × 5) = 2² × 3¹ × 5¹ respectively. LCM of 10 and 60 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 5¹ = 60.
Hence, the LCM of 10 and 60 by prime factorization is 60.

LCM of 10 and 60 by Division Method

To calculate the LCM of 10 and 60 by the division method, we will divide the numbers(10, 60) by their prime factors (preferably common). The product of these divisors gives the LCM of 10 and 60.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 10 and 60. Write this prime number(2) on the left of the given numbers(10 and 60), separated as per the ladder arrangement.
Step 2: If any of the given numbers (10, 60) 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 10 and 60 is the product of all prime numbers on the left, i.e. LCM(10, 60) by division method = 2 × 2 × 3 × 5 = 60.

LCM of 10 and 60 by Listing Multiples

To calculate the LCM of 10 and 60 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 10 (10, 20, 30, 40, 50, . . . ) and 60 (60, 120, 180, 240, . . . . )
Step 2: The common multiples from the multiples of 10 and 60 are 60, 120, . . .
Step 3: The smallest common multiple of 10 and 60 is 60.

∴ The least common multiple of 10 and 60 = 60.

☛ Also Check:

LCM of 10 and 60 Examples

Example 1: The GCD and LCM of two numbers are 10 and 60 respectively. If one number is 10, find the other number.

Solution:

Let the other number be p.
∵ GCD × LCM = 10 × p
⇒ p = (GCD × LCM)/10
⇒ p = (10 × 60)/10
⇒ p = 60
Therefore, the other number is 60.
Example 2: Find the smallest number that is divisible by 10 and 60 exactly.

Solution:

The smallest number that is divisible by 10 and 60 exactly is their LCM.
⇒ Multiples of 10 and 60:
- Multiples of 10 = 10, 20, 30, 40, 50, 60, . . . .
- Multiples of 60 = 60, 120, 180, 240, 300, 360, . . . .
Therefore, the LCM of 10 and 60 is 60.
Example 3: Verify the relationship between GCF and LCM of 10 and 60.

Solution:

The relation between GCF and LCM of 10 and 60 is given as,
LCM(10, 60) × GCF(10, 60) = Product of 10, 60
Prime factorization of 10 and 60 is given as, 10 = (2 × 5) = 2¹ × 5¹ and 60 = (2 × 2 × 3 × 5) = 2² × 3¹ × 5¹
LCM(10, 60) = 60
GCF(10, 60) = 10
LHS = LCM(10, 60) × GCF(10, 60) = 60 × 10 = 600
RHS = Product of 10, 60 = 10 × 60 = 600
⇒ LHS = RHS = 600
Hence, verified.

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FAQs on LCM of 10 and 60

What is the LCM of 10 and 60?

The LCM of 10 and 60 is 60. To find the least common multiple of 10 and 60, we need to find the multiples of 10 and 60 (multiples of 10 = 10, 20, 30, 40 . . . . 60; multiples of 60 = 60, 120, 180, 240) and choose the smallest multiple that is exactly divisible by 10 and 60, i.e., 60.

If the LCM of 60 and 10 is 60, Find its GCF.

LCM(60, 10) × GCF(60, 10) = 60 × 10
Since the LCM of 60 and 10 = 60
⇒ 60 × GCF(60, 10) = 600
Therefore, the greatest common factor (GCF) = 600/60 = 10.

How to Find the LCM of 10 and 60 by Prime Factorization?

To find the LCM of 10 and 60 using prime factorization, we will find the prime factors, (10 = 2 × 5) and (60 = 2 × 2 × 3 × 5). LCM of 10 and 60 is the product of prime factors raised to their respective highest exponent among the numbers 10 and 60.
⇒ LCM of 10, 60 = 2² × 3¹ × 5¹ = 60.

Which of the following is the LCM of 10 and 60? 35, 60, 28, 10

The value of LCM of 10, 60 is the smallest common multiple of 10 and 60. The number satisfying the given condition is 60.

What is the Relation Between GCF and LCM of 10, 60?

The following equation can be used to express the relation between GCF and LCM of 10 and 60, i.e. GCF × LCM = 10 × 60.

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