Least Common Multiple (LCM) of 40 and 169
The least common multiple (LCM) of 40 and 169 is 6760.
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 40 and 169?
First, calculate the GCD of 40 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 169 = 0 remainder 40 |
| 2 | 169 ÷ 40 = 4 remainder 9 |
| 3 | 40 ÷ 9 = 4 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 164 | 5248 |
| 185 and 122 | 22570 |
| 68 and 133 | 9044 |
| 171 and 187 | 31977 |
| 111 and 187 | 20757 |