LCM of 24 and 45

LCM of 24 and 45 is the smallest number among all common multiples of 24 and 45. The first few multiples of 24 and 45 are (24, 48, 72, 96, 120, 144, . . . ) and (45, 90, 135, 180, 225, . . . ) respectively. There are 3 commonly used methods to find LCM of 24 and 45 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 24 and 45 is 360.

Explanation:

The LCM of two non-zero integers, x(24) and y(45), is the smallest positive integer m(360) that is divisible by both x(24) and y(45) without any remainder.

The methods to find the LCM of 24 and 45 are explained below.

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

LCM of 24 and 45 by Division Method

To calculate the LCM of 24 and 45 by the division method, we will divide the numbers(24, 45) by their prime factors (preferably common). The product of these divisors gives the LCM of 24 and 45.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 24 and 45. Write this prime number(2) on the left of the given numbers(24 and 45), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (24, 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 24 and 45 is the product of all prime numbers on the left, i.e. LCM(24, 45) by division method = 2 × 2 × 2 × 3 × 3 × 5 = 360.

LCM of 24 and 45 by Listing Multiples

To calculate the LCM of 24 and 45 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 24 (24, 48, 72, 96, 120, 144, . . . ) and 45 (45, 90, 135, 180, 225, . . . . )
• Step 2: The common multiples from the multiples of 24 and 45 are 360, 720, . . .
• Step 3: The smallest common multiple of 24 and 45 is 360.

∴ The least common multiple of 24 and 45 = 360.

LCM of 24 and 45 by Prime Factorization

Prime factorization of 24 and 45 is (2 × 2 × 2 × 3) = 2³ × 3¹ and (3 × 3 × 5) = 3² × 5¹ respectively. LCM of 24 and 45 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3² × 5¹ = 360.
Hence, the LCM of 24 and 45 by prime factorization is 360.

☛ Also Check:

• LCM of 32 and 80 - 160
• LCM of 9 and 33 - 99
• LCM of 12 and 45 - 180
• LCM of 4, 12 and 16 - 48
• LCM of 8 and 16 - 16
• LCM of 24, 36 and 40 - 360
• LCM of 36, 48 and 72 - 144

FAQs on LCM of 24 and 45

What is the LCM of 24 and 45?

The LCM of 24 and 45 is 360. To find the least common multiple (LCM) of 24 and 45, we need to find the multiples of 24 and 45 (multiples of 24 = 24, 48, 72, 96 . . . . 360; multiples of 45 = 45, 90, 135, 180 . . . . 360) and choose the smallest multiple that is exactly divisible by 24 and 45, i.e., 360.

If the LCM of 45 and 24 is 360, Find its GCF.

LCM(45, 24) × GCF(45, 24) = 45 × 24
Since the LCM of 45 and 24 = 360
⇒ 360 × GCF(45, 24) = 1080
Therefore, the greatest common factor (GCF) = 1080/360 = 3.

What is the Least Perfect Square Divisible by 24 and 45?

The least number divisible by 24 and 45 = LCM(24, 45)
LCM of 24 and 45 = 2 × 2 × 2 × 3 × 3 × 5 [Incomplete pair(s): 2, 5]
⇒ Least perfect square divisible by each 24 and 45 = LCM(24, 45) × 2 × 5 = 3600 [Square root of 3600 = √3600 = ±60]
Therefore, 3600 is the required number.

What is the Relation Between GCF and LCM of 24, 45?

The following equation can be used to express the relation between GCF and LCM of 24 and 45, i.e. GCF × LCM = 24 × 45.

How to Find the LCM of 24 and 45 by Prime Factorization?

To find the LCM of 24 and 45 using prime factorization, we will find the prime factors, (24 = 2 × 2 × 2 × 3) and (45 = 3 × 3 × 5). LCM of 24 and 45 is the product of prime factors raised to their respective highest exponent among the numbers 24 and 45.
⇒ LCM of 24, 45 = 2³ × 3² × 5¹ = 360.