Least Common Multiple (LCM) of 142 and 169
The least common multiple (LCM) of 142 and 169 is 23998.
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 142 and 169?
First, calculate the GCD of 142 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 142 ÷ 169 = 0 remainder 142 |
| 2 | 169 ÷ 142 = 1 remainder 27 |
| 3 | 142 ÷ 27 = 5 remainder 7 |
| 4 | 27 ÷ 7 = 3 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 157 | 2198 |
| 146 and 97 | 14162 |
| 101 and 44 | 4444 |
| 189 and 132 | 8316 |
| 190 and 163 | 30970 |