what is the least common multiple of 8,10
LCM
Solve by writing the multiples.
8 > 8,16,24,32,40,48,56,64,....
10 > 10,20,30,40,50,60,......
Solve by prime factorization.
8 10
/ \ / \
2•4 2•5
\•/\
2•2•2
2•2•2•5 = ?
To find the least common multiple (LCM) of two numbers, you need to find the smallest number that is divisible by both of the given numbers without leaving any remainders.
To find the LCM of 8 and 10, you can start by listing the multiples of each number and finding the smallest common multiple:
Multiples of 8: 8, 16, 24, 32, 40, ...
Multiples of 10: 10, 20, 30, 40, 50, ...
From the list, you can see that the smallest number that appears in both lists is 40. Therefore, the least common multiple of 8 and 10 is 40.
Alternatively, you can also use a common method to find the LCM using prime factorization:
Step 1: Prime factorize each number:
- 8 = 2 x 2 x 2
- 10 = 2 x 5
Step 2: Write down the highest power of each prime factor:
- 2^3 x 5^1
Step 3: Multiply the highest powers together:
- 2^3 x 5^1 = 8 x 5 = 40
Therefore, the least common multiple (LCM) of 8 and 10 is 40.
Which of these multiples is also divisible by 8?
10, 20, 30, 40, 50, 60, 70