LCM of 10 and 24

LCM of 10 and 24 is the smallest number among all common multiples of 10 and 24. The first few multiples of 10 and 24 are (10, 20, 30, 40, . . . ) and (24, 48, 72, 96, 120, 144, . . . ) respectively. There are 3 commonly used methods to find LCM of 10 and 24 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 10 and 24 is 120.

Explanation:

The LCM of two non-zero integers, x(10) and y(24), is the smallest positive integer m(120) that is divisible by both x(10) and y(24) without any remainder.

The methods to find the LCM of 10 and 24 are explained below.

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

LCM of 10 and 24 by Listing Multiples

To calculate the LCM of 10 and 24 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, . . . ) and 24 (24, 48, 72, 96, 120, 144, . . . . )
• Step 2: The common multiples from the multiples of 10 and 24 are 120, 240, . . .
• Step 3: The smallest common multiple of 10 and 24 is 120.

∴ The least common multiple of 10 and 24 = 120.

LCM of 10 and 24 by Prime Factorization

Prime factorization of 10 and 24 is (2 × 5) = 2¹ × 5¹ and (2 × 2 × 2 × 3) = 2³ × 3¹ respectively. LCM of 10 and 24 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3¹ × 5¹ = 120.
Hence, the LCM of 10 and 24 by prime factorization is 120.

LCM of 10 and 24 by Division Method

To calculate the LCM of 10 and 24 by the division method, we will divide the numbers(10, 24) by their prime factors (preferably common). The product of these divisors gives the LCM of 10 and 24.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 10 and 24. Write this prime number(2) on the left of the given numbers(10 and 24), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (10, 24) 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 24 is the product of all prime numbers on the left, i.e. LCM(10, 24) by division method = 2 × 2 × 2 × 3 × 5 = 120.

☛ Also Check:

• LCM of 6 and 27 - 54
• LCM of 6 and 21 - 42
• LCM of 6 and 20 - 60
• LCM of 6 and 18 - 18
• LCM of 6 and 16 - 48
• LCM of 6 and 15 - 30
• LCM of 6 and 14 - 42

FAQs on LCM of 10 and 24

What is the LCM of 10 and 24?

The LCM of 10 and 24 is 120. To find the LCM (least common multiple) of 10 and 24, we need to find the multiples of 10 and 24 (multiples of 10 = 10, 20, 30, 40 . . . . 120; multiples of 24 = 24, 48, 72, 96 . . . . 120) and choose the smallest multiple that is exactly divisible by 10 and 24, i.e., 120.

What are the Methods to Find LCM of 10 and 24?

The commonly used methods to find the LCM of 10 and 24 are:

• Division Method
• Prime Factorization Method
• Listing Multiples

If the LCM of 24 and 10 is 120, Find its GCF.

LCM(24, 10) × GCF(24, 10) = 24 × 10
Since the LCM of 24 and 10 = 120
⇒ 120 × GCF(24, 10) = 240
Therefore, the greatest common factor (GCF) = 240/120 = 2.

What is the Least Perfect Square Divisible by 10 and 24?

The least number divisible by 10 and 24 = LCM(10, 24)
LCM of 10 and 24 = 2 × 2 × 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5]
⇒ Least perfect square divisible by each 10 and 24 = LCM(10, 24) × 2 × 3 × 5 = 3600 [Square root of 3600 = √3600 = ±60]
Therefore, 3600 is the required number.

How to Find the LCM of 10 and 24 by Prime Factorization?

To find the LCM of 10 and 24 using prime factorization, we will find the prime factors, (10 = 2 × 5) and (24 = 2 × 2 × 2 × 3). LCM of 10 and 24 is the product of prime factors raised to their respective highest exponent among the numbers 10 and 24.
⇒ LCM of 10, 24 = 2³ × 3¹ × 5¹ = 120.