Least Common Multiple (LCM) of 169 and 36
The least common multiple (LCM) of 169 and 36 is 6084.
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 36?
First, calculate the GCD of 169 and 36 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 36 = 4 remainder 25 |
| 2 | 36 ÷ 25 = 1 remainder 11 |
| 3 | 25 ÷ 11 = 2 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 16 | 368 |
| 178 and 91 | 16198 |
| 66 and 51 | 1122 |
| 176 and 140 | 6160 |
| 98 and 133 | 1862 |