LCM of 24 and 56

The common multiple of 24 and 56 is 168.  Here, we will learn about the LCM of 2 numbers. Children learn about LCM at younger ages. Here, let’s discuss the methods used to find the LCM.

Out of many methods, the prime factorization method is widely used for its easy approach. Here, we will learn about other methods as well. A few commonly used methods are as follows - 

1. Listing Of Multiples
2. Prime Factorization
3. Division Method
    

Listing multiples can be a tedious method for finding the LCM. Here, the listing of multiples for all these 2 numbers is noted - 

• Multiples Of 24: 24, 48, 72, 96, 120, 144, 168
• Multiples of 56: 56, 112, 168, 224, 280, 336, 392,
• Then we can see that, out of 24 and 56, 168 is the smallest common number that is present in them. So we see that 168 is the LCM of 24 and 56.

The product of the highest power of prime factors of 24 and 56 is the LCM of these numbers. So let us look at it step by step to understand it better.

Breaking the given numbers into their prime factors.

• Prime factorization of 24= 2³ × 3¹
• Prime factorization of 56 = 2 x 2x 2x7

Multiplying the highest power of prime factors: 2³ x3¹ x7¹

LCM of 24 and 56 is 168
 

In this method, we will be dividing the given numbers with the common prime factors until all numbers are reduced to 1. Let us look at this step by step and make it easy for the children to learn it.

Step 1: Arrange the numbers in a sequence, with divisors, on the left and numbers on the right sides.

Step 2: For finding the divisor, it is always the smallest common prime factor. Here, the smallest common prime factor is 2. Dividing 24 and 56 by 2. The result is 12 and 28.

Step 3: As 12 and 28 are divisible by 2, again the divisor is 2. Dividing 6 and 14 by 2. Now the result is 3 and 7.

Step 4: Continue dividing the numbers with the smallest prime number until all numbers are reduced to 1.

The divisors are 2, 2, 2, 3, 7 LCM of 24 and 56 is the product of divisors.

Hence, the LCM of (24 and 56) = 2 × 2 × 2 × 3 × 7 = 168
 

• Factor: A number that will divide two or more numbers, leaving no remainder. For 18 and 24 we have 6 as a common factor, it means both 18 and 24 can be divisible by 6.

• Prime Factorization: When a number can be represented as the factors of prime numbers, it is called prime factorization. The prime factorization of 18 for example is 2×3×3.

• Greatest Common Factor (GCF): GCF is the greatest factor that is common in the given numbers. For example, the GCF of 5, 10, and 15 is 5. Because the common factors of 5 and 10 are 1 and 5.

• Division Method: In the division method, the numbers are divided by the smallest common prime factor till the numbers are reduced to 1.