LCM of 10 and 45

LCM of 10 and 45 is the smallest number among all common multiples of 10 and 45. The first few multiples of 10 and 45 are (10, 20, 30, 40, 50, 60, . . . ) and (45, 90, 135, 180, 225, . . . ) respectively. There are 3 commonly used methods to find LCM of 10 and 45 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 10 and 45 is 90.

Explanation:

The LCM of two non-zero integers, x(10) and y(45), is the smallest positive integer m(90) that is divisible by both x(10) and y(45) without any remainder.

The methods to find the LCM of 10 and 45 are explained below.

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

LCM of 10 and 45 by Division Method

To calculate the LCM of 10 and 45 by the division method, we will divide the numbers(10, 45) by their prime factors (preferably common). The product of these divisors gives the LCM of 10 and 45.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 10 and 45. Write this prime number(2) on the left of the given numbers(10 and 45), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (10, 45) 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 45 is the product of all prime numbers on the left, i.e. LCM(10, 45) by division method = 2 × 3 × 3 × 5 = 90.

LCM of 10 and 45 by Prime Factorization

Prime factorization of 10 and 45 is (2 × 5) = 2¹ × 5¹ and (3 × 3 × 5) = 3² × 5¹ respectively. LCM of 10 and 45 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3² × 5¹ = 90.
Hence, the LCM of 10 and 45 by prime factorization is 90.

LCM of 10 and 45 by Listing Multiples

To calculate the LCM of 10 and 45 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, . . . ) and 45 (45, 90, 135, 180, 225, . . . . )
• Step 2: The common multiples from the multiples of 10 and 45 are 90, 180, . . .
• Step 3: The smallest common multiple of 10 and 45 is 90.

∴ The least common multiple of 10 and 45 = 90.

☛ Also Check:

• LCM of 5 and 11 - 55
• LCM of 5 and 10 - 10
• LCM of 49 and 63 - 441
• LCM of 48 and 72 - 144
• LCM of 48 and 64 - 192
• LCM of 48 and 60 - 240
• LCM of 48 and 56 - 336

FAQs on LCM of 10 and 45

What is the LCM of 10 and 45?

The LCM of 10 and 45 is 90. To find the least common multiple (LCM) of 10 and 45, we need to find the multiples of 10 and 45 (multiples of 10 = 10, 20, 30, 40 . . . . 90; multiples of 45 = 45, 90, 135, 180) and choose the smallest multiple that is exactly divisible by 10 and 45, i.e., 90.

What are the Methods to Find LCM of 10 and 45?

The commonly used methods to find the LCM of 10 and 45 are:

• Division Method
• Prime Factorization Method
• Listing Multiples

What is the Relation Between GCF and LCM of 10, 45?

The following equation can be used to express the relation between GCF and LCM of 10 and 45, i.e. GCF × LCM = 10 × 45.

Which of the following is the LCM of 10 and 45? 35, 12, 24, 90

The value of LCM of 10, 45 is the smallest common multiple of 10 and 45. The number satisfying the given condition is 90.

If the LCM of 45 and 10 is 90, Find its GCF.

LCM(45, 10) × GCF(45, 10) = 45 × 10
Since the LCM of 45 and 10 = 90
⇒ 90 × GCF(45, 10) = 450
Therefore, the GCF = 450/90 = 5.