Least Common Multiple (LCM) of 169 and 188
The least common multiple (LCM) of 169 and 188 is 31772.
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 169 and 188?
First, calculate the GCD of 169 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 188 = 0 remainder 169 |
| 2 | 188 ÷ 169 = 1 remainder 19 |
| 3 | 169 ÷ 19 = 8 remainder 17 |
| 4 | 19 ÷ 17 = 1 remainder 2 |
| 5 | 17 ÷ 2 = 8 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 98 | 6762 |
| 119 and 157 | 18683 |
| 162 and 107 | 17334 |
| 77 and 117 | 9009 |
| 90 and 158 | 7110 |