LCM of 10 and 100

LCM of 10 and 100 is the smallest number among all common multiples of 10 and 100. The first few multiples of 10 and 100 are (10, 20, 30, 40, 50, 60, 70, . . . ) and (100, 200, 300, 400, 500, . . . ) respectively. There are 3 commonly used methods to find LCM of 10 and 100 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 10 and 100 is 100.

Explanation:

The LCM of two non-zero integers, x(10) and y(100), is the smallest positive integer m(100) that is divisible by both x(10) and y(100) without any remainder.

Let's look at the different methods for finding the LCM of 10 and 100.

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

LCM of 10 and 100 by Listing Multiples

To calculate the LCM of 10 and 100 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, 60, 70, . . . ) and 100 (100, 200, 300, 400, 500, . . . . )
• Step 2: The common multiples from the multiples of 10 and 100 are 100, 200, . . .
• Step 3: The smallest common multiple of 10 and 100 is 100.

∴ The least common multiple of 10 and 100 = 100.

LCM of 10 and 100 by Division Method

To calculate the LCM of 10 and 100 by the division method, we will divide the numbers(10, 100) by their prime factors (preferably common). The product of these divisors gives the LCM of 10 and 100.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 10 and 100. Write this prime number(2) on the left of the given numbers(10 and 100), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (10, 100) 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 100 is the product of all prime numbers on the left, i.e. LCM(10, 100) by division method = 2 × 2 × 5 × 5 = 100.

LCM of 10 and 100 by Prime Factorization

Prime factorization of 10 and 100 is (2 × 5) = 2¹ × 5¹ and (2 × 2 × 5 × 5) = 2² × 5² respectively. LCM of 10 and 100 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 5² = 100.
Hence, the LCM of 10 and 100 by prime factorization is 100.

☛ Also Check:

• LCM of 80 and 120 - 240
• LCM of 8 and 9 - 72
• LCM of 8 and 64 - 64
• LCM of 8 and 56 - 56
• LCM of 8 and 42 - 168
• LCM of 8 and 36 - 72
• LCM of 8 and 32 - 32

FAQs on LCM of 10 and 100

What is the LCM of 10 and 100?

The LCM of 10 and 100 is 100. To find the least common multiple of 10 and 100, we need to find the multiples of 10 and 100 (multiples of 10 = 10, 20, 30, 40 . . . . 100; multiples of 100 = 100, 200, 300, 400) and choose the smallest multiple that is exactly divisible by 10 and 100, i.e., 100.

How to Find the LCM of 10 and 100 by Prime Factorization?

To find the LCM of 10 and 100 using prime factorization, we will find the prime factors, (10 = 2 × 5) and (100 = 2 × 2 × 5 × 5). LCM of 10 and 100 is the product of prime factors raised to their respective highest exponent among the numbers 10 and 100.
⇒ LCM of 10, 100 = 2² × 5² = 100.

What are the Methods to Find LCM of 10 and 100?

The commonly used methods to find the LCM of 10 and 100 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

If the LCM of 100 and 10 is 100, Find its GCF.

LCM(100, 10) × GCF(100, 10) = 100 × 10
Since the LCM of 100 and 10 = 100
⇒ 100 × GCF(100, 10) = 1000
Therefore, the greatest common factor = 1000/100 = 10.

What is the Relation Between GCF and LCM of 10, 100?

The following equation can be used to express the relation between GCF and LCM of 10 and 100, i.e. GCF × LCM = 10 × 100.