Least Common Multiple (LCM) of 55 and 133
The least common multiple (LCM) of 55 and 133 is 7315.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 55 and 133?
First, calculate the GCD of 55 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 133 = 0 remainder 55 |
| 2 | 133 ÷ 55 = 2 remainder 23 |
| 3 | 55 ÷ 23 = 2 remainder 9 |
| 4 | 23 ÷ 9 = 2 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 155 | 22940 |
| 136 and 152 | 2584 |
| 44 and 50 | 1100 |
| 14 and 114 | 798 |
| 118 and 105 | 12390 |