Least Common Multiple (LCM) of 101 and 189
The least common multiple (LCM) of 101 and 189 is 19089.
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 189?
First, calculate the GCD of 101 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 189 = 0 remainder 101 |
| 2 | 189 ÷ 101 = 1 remainder 88 |
| 3 | 101 ÷ 88 = 1 remainder 13 |
| 4 | 88 ÷ 13 = 6 remainder 10 |
| 5 | 13 ÷ 10 = 1 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 61 | 7869 |
| 143 and 135 | 19305 |
| 169 and 180 | 30420 |
| 158 and 128 | 10112 |
| 189 and 173 | 32697 |