Least Common Multiple (LCM) of 58 and 169
The least common multiple (LCM) of 58 and 169 is 9802.
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 58 and 169?
First, calculate the GCD of 58 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 58 ÷ 169 = 0 remainder 58 |
| 2 | 169 ÷ 58 = 2 remainder 53 |
| 3 | 58 ÷ 53 = 1 remainder 5 |
| 4 | 53 ÷ 5 = 10 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 192 | 960 |
| 140 and 180 | 1260 |
| 86 and 20 | 860 |
| 106 and 96 | 5088 |
| 31 and 70 | 2170 |