Least Common Multiple (LCM) of 29 and 169
The least common multiple (LCM) of 29 and 169 is 4901.
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 29 and 169?
First, calculate the GCD of 29 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 169 = 0 remainder 29 |
| 2 | 169 ÷ 29 = 5 remainder 24 |
| 3 | 29 ÷ 24 = 1 remainder 5 |
| 4 | 24 ÷ 5 = 4 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 115 | 15985 |
| 177 and 188 | 33276 |
| 109 and 162 | 17658 |
| 167 and 198 | 33066 |
| 92 and 60 | 1380 |