Lcm Of 8 And 10 Update

The LCM (Least Common Multiple) of 8 and 10 is 40.

To find the LCM of two numbers, we can use different methods like Prime Factorization method, Listing Multiples method, or Division method.

Using the Prime Factorization method:

Step 1: Find the prime factors of each number

• 8 can be written as 2 x 2 x 2
• 10 can be written as 2 x 5

Step 2: Write down all the prime factors with the highest power of each factor

• 2^3 x 5 = 40

Therefore, the LCM of 8 and 10 is 40.

Using the Listing Multiples method:

Step 1: List the multiples of each number until you find a common multiple

• Multiples of 8: 8, 16, 24, 32, 40
• Multiples of 10: 10, 20, 30, 40

Step 2: Identify the smallest common multiple from the lists

• 40 is the smallest common multiple

Therefore, the LCM of 8 and 10 is 40.

Using the Division method:

Step 1: Divide the larger number by the smaller number

• 10 ÷ 8 = 1 with a remainder of 2

Step 2: Divide the smaller number by the remainder

• 8 ÷ 2 = 4

Step 3: Multiply the larger number by the quotient and the remainder

• 10 x 4 x 2 = 40

Therefore, the LCM of 8 and 10 is 40.

To find the LCM (Least Common Multiple) and GCF (Greatest Common Factor) of 8 and 10, we first need to find their prime factors:

• 8 = 2 x 2 x 2
• 10 = 2 x 5

To find the GCF, we take the product of the common prime factors with the lowest exponent, which is only the factor of 2 in this case:
GCF(8, 10) = 2

To find the LCM, we take the product of all the prime factors, each raised to the highest exponent it appears in either number:
LCM(8, 10) = 2 x 2 x 2 x 5 = 40

Therefore, the GCF of 8 and 10 is 2, and the LCM of 8 and 10 is 40.

LCM stands for “Least Common Multiple.” It is the smallest positive integer that is a multiple of two or more given numbers. Here’s how to calculate LCM:

Method 1: Prime Factorization

Step 1: Write the prime factorization of each number.

Step 2: Identify the highest power of each prime factor that appears in any of the factorizations.

Step 3: Multiply these highest powers together to get the LCM.

Example:
Find the LCM of 12, 20, and 30.

Step 1: Prime factorization of 12: 2 × 2 × 3
Prime factorization of 20: 2 × 2 × 5
Prime factorization of 30: 2 × 3 × 5

Step 2: The highest power of 2 that appears in any of the factorizations is 2^2 = 4.
The highest power of 3 that appears in any of the factorizations is 3^1 = 3.
The highest power of 5 that appears in any of the factorizations is 5^1 = 5.

Step 3: LCM = 2^2 × 3 × 5 = 60.

Therefore, the LCM of 12, 20, and 30 is 60.

Method 2: Division Method

Step 1: Write the given numbers in a vertical column.

Step 2: Divide the numbers by the smallest prime number that divides at least one of them, and write the quotient and the remainder next to the original number.

Step 3: Repeat step 2 with the new column until all the numbers in the column are prime numbers.

Step 4: Multiply the prime numbers and any remaining factors to get the LCM.

Example:
Find the LCM of 12, 20, and 30.

Step 1: Write the numbers in a vertical column.

 | 12
 | 20
 | 30

Step 2: Divide by the smallest prime number that divides at least one of the numbers.

 |  2   6
 |  2  10
 |  3  10

Step 3: Repeat step 2 with the new column until all the numbers in the column are prime.

 |  2  3  3
 |  2  5  1
 |  3  5  1

Step 4: Multiply the prime numbers and any remaining factors to get the LCM.

LCM = 2 × 2 × 3 × 3 × 5 = 180.

Therefore, the LCM of 12, 20, and 30 is 180.

The highest common factor (HCF) of 10 and 8 is 2.

To find the HCF, we can list out the factors of each number and find the largest factor that they have in common.

Factors of 10: 1, 2, 5, 10
Factors of 8: 1, 2, 4, 8

The largest factor that 10 and 8 have in common is 2, therefore the HCF of 10 and 8 is 2.

The LCM (Least Common Multiple) of any two equal numbers is the number itself. Therefore, the LCM of 8 and 8 is 8.

To find the LCM (Least Common Multiple) of 8, 10, and 12, we need to find the smallest number that is divisible by all three given numbers.

First, we can write the prime factorization of each number:

• 8 = 2 x 2 x 2
• 10 = 2 x 5
• 12 = 2 x 2 x 3

Next, we need to find the highest power of each prime factor that appears in any of the factorizations. In this case, the highest power of 2 that appears is 2 x 2 x 2 = 8, the highest power of 3 that appears is 3, and the highest power of 5 that appears is 5.

Finally, we can find the LCM by multiplying the highest powers of each prime factor:

LCM(8, 10, 12) = 2 x 2 x 2 x 3 x 5 = 120

Therefore, the LCM of 8, 10, and 12 is 120.