The number 108 is the LCM of 36 and 54. list the next multiple of 36 and 54. Explain your reasoning
72 based on 4x9 is 36 and 6x9 is 54 the next even number would be 8, so 8x9 is 72.
Well, 108 being the LCM of 36 and 54 means it's the smallest number that both 36 and 54 can divide into evenly. To find the next multiple of 36, we simply need to keep adding 36 to 108. So, 108 + 36 equals 144, which is the next multiple of 36.
Now, to find the next multiple of 54, we do the same thing. We start with 108 and keep adding 54. So, 108 + 54 equals 162, which is the next multiple of 54.
There you have it! The next multiple of 36 is 144, and the next multiple of 54 is 162. Why did they attend the party together? Because they heard it was going to be an "even-ing"!
To find the next multiple of 36 and 54 after the number 108, we need to find the least common multiple (LCM) of these two numbers.
The LCM of 36 and 54 is the smallest number that is divisible by both 36 and 54 without leaving a remainder. To find the LCM, we can use the prime factorization method.
Step 1: Prime factorization of 36:
- 36 can be expressed as 2^2 * 3^2.
Step 2: Prime factorization of 54:
- 54 can be expressed as 2 * 3^3.
Step 3: Take the highest power of each prime factor:
- The highest power of 2 is 2^2.
- The highest power of 3 is 3^3.
Step 4: Multiply the highest powers of the prime factors:
- LCM = 2^2 * 3^3 = 4 * 27 = 108.
So we have found that the LCM of 36 and 54 is 108. The next multiple of 36 and 54 would be obtained by multiplying 108 by any positive integer.
Therefore, the next multiple of 36 and 54 after 108 is 108 multiplied by any positive integer, such as 108 * 2, which equals 216.
To find the next multiple of 36 and 54, we need to understand what a multiple is. A multiple is a number that can be evenly divided by another number without leaving a remainder.
To find the next multiple of 36, we can start by multiplying it by 2.
36 x 2 = 72
Therefore, the next multiple of 36 is 72.
For 54, we can apply the same logic. Multiply it by 2:
54 x 2 = 108
However, 108 is already given as the LCM (Least Common Multiple) of 36 and 54. So, we need to find the next multiple of 54.
To do this, we multiply it by 3:
54 x 3 = 162
Therefore, the next multiple of 54 is 162.
In summary, the next multiple of 36 is 72, and the next multiple of 54 is 162. We found these by identifying the LCM and then multiplying each number by the next possible factor.