Least Common Multiple (LCM) of 36 and 169
The least common multiple (LCM) of 36 and 169 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 36 and 169?
First, calculate the GCD of 36 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 169 = 0 remainder 36 |
| 2 | 169 ÷ 36 = 4 remainder 25 |
| 3 | 36 ÷ 25 = 1 remainder 11 |
| 4 | 25 ÷ 11 = 2 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 20 | 780 |
| 104 and 70 | 3640 |
| 199 and 178 | 35422 |
| 135 and 89 | 12015 |
| 67 and 108 | 7236 |