Least Common Multiple (LCM) of 169 and 192
The least common multiple (LCM) of 169 and 192 is 32448.
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 192?
First, calculate the GCD of 169 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 192 = 0 remainder 169 |
| 2 | 192 ÷ 169 = 1 remainder 23 |
| 3 | 169 ÷ 23 = 7 remainder 8 |
| 4 | 23 ÷ 8 = 2 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 15 | 615 |
| 78 and 178 | 6942 |
| 120 and 99 | 3960 |
| 12 and 160 | 480 |
| 111 and 37 | 111 |