Least Common Multiple (LCM) of 178 and 169
The least common multiple (LCM) of 178 and 169 is 30082.
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 178 and 169?
First, calculate the GCD of 178 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 169 = 1 remainder 9 |
| 2 | 169 ÷ 9 = 18 remainder 7 |
| 3 | 9 ÷ 7 = 1 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 120 | 7080 |
| 179 and 46 | 8234 |
| 83 and 101 | 8383 |
| 77 and 156 | 12012 |
| 60 and 118 | 3540 |