Least Common Multiple (LCM) of 55 and 143
The least common multiple (LCM) of 55 and 143 is 715.
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 143?
First, calculate the GCD of 55 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 143 = 0 remainder 55 |
| 2 | 143 ÷ 55 = 2 remainder 33 |
| 3 | 55 ÷ 33 = 1 remainder 22 |
| 4 | 33 ÷ 22 = 1 remainder 11 |
| 5 | 22 ÷ 11 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 72 | 1224 |
| 35 and 129 | 4515 |
| 70 and 66 | 2310 |
| 65 and 11 | 715 |
| 174 and 99 | 5742 |