LCM(55, 8)
The LCM of 55 and 8 is 440.
To find the least common multiple (LCM) of 55 and 8, you can use the prime factorization method or the listing method.
Prime factorization method:
1. Start by finding the prime factors of each number.
- The prime factorization of 55 is 5 x 11.
- The prime factorization of 8 is 2 x 2 x 2.
2. Write down all the prime factors, including duplicates, and choose the highest exponent for each factor.
- The prime factors for 55 are 2, 5, and 11.
- The prime factors for 8 are 2.
- The highest exponent for 2 is 3, for 5 is 1, and for 11 is 1.
3. Multiply all the prime factors together, raised to their respective exponents.
- LCM(55, 8) = 2^3 x 5^1 x 11^1 = 440.
Listing method:
1. List the multiples of each number until you find a common multiple.
- Multiples of 55: 55, 110, 165, 220, 275, 330, 385, 440...
- Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120...
2. Based on the list above, you can see that 440 is the smallest number that appears in both lists. Therefore, the LCM of 55 and 8 is 440.
So, the LCM of 55 and 8 is 440.
To find the least common multiple (LCM) of 55 and 8, we can use the prime factorization method or the method of finding multiples.
Method 1: Prime Factorization
Step 1: Find the prime factorization of each number.
Prime factorization of 55: 55 = 5 * 11
Prime factorization of 8: 8 = 2^3
Step 2: Take the highest power of each factor that appears in either factorization.
LCM = 2^3 * 5 * 11 = 440
Method 2: Finding Multiples
Step 1: List the multiples of each number until you find a common multiple:
Multiples of 55: 55, 110, 165, 220, 275, 330, 385, 440
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376, 384, 392, 400, 408, 416, 424, 432, 440
Step 2: Find the least common multiple from the list of common multiples.
The least common multiple (LCM) of 55 and 8 is 440.