Least Common Multiple (LCM) of 101 and 155
The least common multiple (LCM) of 101 and 155 is 15655.
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 101 and 155?
First, calculate the GCD of 101 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 155 = 0 remainder 101 |
| 2 | 155 ÷ 101 = 1 remainder 54 |
| 3 | 101 ÷ 54 = 1 remainder 47 |
| 4 | 54 ÷ 47 = 1 remainder 7 |
| 5 | 47 ÷ 7 = 6 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 115 | 13110 |
| 59 and 199 | 11741 |
| 165 and 83 | 13695 |
| 171 and 88 | 15048 |
| 163 and 105 | 17115 |