Least Common Multiple (LCM) of 169 and 67
The least common multiple (LCM) of 169 and 67 is 11323.
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 169 and 67?
First, calculate the GCD of 169 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 67 = 2 remainder 35 |
| 2 | 67 ÷ 35 = 1 remainder 32 |
| 3 | 35 ÷ 32 = 1 remainder 3 |
| 4 | 32 ÷ 3 = 10 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 153 | 6120 |
| 114 and 168 | 3192 |
| 111 and 59 | 6549 |
| 130 and 194 | 12610 |
| 71 and 40 | 2840 |