LCM of 45 and 75

LCM of 45 and 75 is the smallest number among all common multiples of 45 and 75. The first few multiples of 45 and 75 are (45, 90, 135, 180, 225, 270, 315, . . . ) and (75, 150, 225, 300, 375, . . . ) respectively. There are 3 commonly used methods to find LCM of 45 and 75 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 45 and 75 is 225.

Explanation:

The LCM of two non-zero integers, x(45) and y(75), is the smallest positive integer m(225) that is divisible by both x(45) and y(75) without any remainder.

The methods to find the LCM of 45 and 75 are explained below.

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

LCM of 45 and 75 by Listing Multiples

To calculate the LCM of 45 and 75 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 45 (45, 90, 135, 180, 225, 270, 315, . . . ) and 75 (75, 150, 225, 300, 375, . . . . )
• Step 2: The common multiples from the multiples of 45 and 75 are 225, 450, . . .
• Step 3: The smallest common multiple of 45 and 75 is 225.

∴ The least common multiple of 45 and 75 = 225.

LCM of 45 and 75 by Division Method

To calculate the LCM of 45 and 75 by the division method, we will divide the numbers(45, 75) by their prime factors (preferably common). The product of these divisors gives the LCM of 45 and 75.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 45 and 75. Write this prime number(3) on the left of the given numbers(45 and 75), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (45, 75) 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 45 and 75 is the product of all prime numbers on the left, i.e. LCM(45, 75) by division method = 3 × 3 × 5 × 5 = 225.

LCM of 45 and 75 by Prime Factorization

Prime factorization of 45 and 75 is (3 × 3 × 5) = 3² × 5¹ and (3 × 5 × 5) = 3¹ × 5² respectively. LCM of 45 and 75 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3² × 5² = 225.
Hence, the LCM of 45 and 75 by prime factorization is 225.

☛ Also Check:

• LCM of 15 and 90 - 90
• LCM of 25 and 65 - 325
• LCM of 3 and 6 - 6
• LCM of 8, 9 and 25 - 1800
• LCM of 35 and 55 - 385
• LCM of 18 and 48 - 144
• LCM of 12 and 27 - 108

FAQs on LCM of 45 and 75

What is the LCM of 45 and 75?

The LCM of 45 and 75 is 225. To find the least common multiple (LCM) of 45 and 75, we need to find the multiples of 45 and 75 (multiples of 45 = 45, 90, 135, 180 . . . . 225; multiples of 75 = 75, 150, 225, 300) and choose the smallest multiple that is exactly divisible by 45 and 75, i.e., 225.

What are the Methods to Find LCM of 45 and 75?

The commonly used methods to find the LCM of 45 and 75 are:

• Division Method
• Listing Multiples
• Prime Factorization Method

If the LCM of 75 and 45 is 225, Find its GCF.

LCM(75, 45) × GCF(75, 45) = 75 × 45
Since the LCM of 75 and 45 = 225
⇒ 225 × GCF(75, 45) = 3375
Therefore, the greatest common factor (GCF) = 3375/225 = 15.

Which of the following is the LCM of 45 and 75? 225, 15, 32, 45

The value of LCM of 45, 75 is the smallest common multiple of 45 and 75. The number satisfying the given condition is 225.

What is the Least Perfect Square Divisible by 45 and 75?

The least number divisible by 45 and 75 = LCM(45, 75)
LCM of 45 and 75 = 3 × 3 × 5 × 5 [No incomplete pair]
⇒ Least perfect square divisible by each 45 and 75 = 225 [Square root of 225 = √225 = ±15]
Therefore, 225 is the required number.