Least Common Multiple (LCM) of 192 and 169
The least common multiple (LCM) of 192 and 169 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 192 and 169?
First, calculate the GCD of 192 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 169 = 1 remainder 23 |
| 2 | 169 ÷ 23 = 7 remainder 8 |
| 3 | 23 ÷ 8 = 2 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 13 | 546 |
| 120 and 199 | 23880 |
| 175 and 189 | 4725 |
| 124 and 103 | 12772 |
| 155 and 140 | 4340 |