Question

what is the LCM of 10 and 24 by division method?​

Answer 1

Answer:

The Least Common Multiple (LCM) is also referred to as the Lowest Common Multiple (LCM) and Least Common Divisor (LCD). For two integers a and b, denoted LCM(a,b), the LCM is the smallest positive integer that is evenly divisible by both a and b. For example, LCM(2,3) = 6 and LCM(6,10) = 30.

The LCM of two or more numbers is the smallest number that is evenly divisible by all numbers in the set.

Least Common Multiple Calculator

Find the LCM of a set of numbers with this calculator which also shows the steps and how to do the work.

Input the numbers you want to find the LCM for. You can use commas or spaces to separate your numbers. But do not use commas within your numbers. For example, enter 2500, 1000 and not 2,500, 1,000.

How to Find the Least Common Multiple LCM

This LCM calculator with steps finds the LCM and shows the work using 5 different methods:

Listing Multiples

Prime Factorization

Cake/Ladder Method

Division Method

Using the Greatest Common Factor GCF

How to Find LCM by Listing Multiples

List the multiples of each number until at least one of the multiples appears on all lists

Find the smallest number that is on all of the lists

This number is the LCM

Example: LCM(6,7,21)

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

Multiples of 7: 7, 14, 21, 28, 35, 42, 56, 63

Multiples of 21: 21, 42, 63

Find the smallest number that is on all of the lists. We have it in bold above.

So LCM(6, 7, 21) is 42

How to find LCM by Prime Factorization

Find all the prime factors of each given number.

List all the prime numbers found, as many times as they occur most often for any one given number.

Multiply the list of prime factors together to find the LCM.

The LCM(a,b) is calculated by finding the prime factorization of both a and b. Use the same process for the LCM of more than 2 numbers.

For example, for LCM(12,30) we find:

Prime factorization of 12 = 2 × 2 × 3

Prime factorization of 30 = 2 × 3 × 5

Using all prime numbers found as often as each occurs most often we take 2 × 2 × 3 × 5 = 60

Therefore LCM(12,30) = 60.

For example, for LCM(24,300) we find:

Prime factorization of 24 = 2 × 2 × 2 × 3

Prime factorization of 300 = 2 × 2 × 3 × 5 × 5

Using all prime numbers found as often as each occurs most often we take 2 × 2 × 2 × 3 × 5 × 5 = 600

Therefore LCM(24,300) = 600.

Answer 2

Answer:

120

Step-by-step explanation:

2 | 10 | 24

5 | 5 | 12

2 | 1 | 6

2 | 1 | 3

3 | 1 | 1

Lcm = 2×5×2×2×3

= 120