Least Common Multiple (LCM) of 169 and 37
The least common multiple (LCM) of 169 and 37 is 6253.
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 37?
First, calculate the GCD of 169 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 37 = 4 remainder 21 |
| 2 | 37 ÷ 21 = 1 remainder 16 |
| 3 | 21 ÷ 16 = 1 remainder 5 |
| 4 | 16 ÷ 5 = 3 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 119 | 6307 |
| 155 and 68 | 10540 |
| 106 and 54 | 2862 |
| 49 and 51 | 2499 |
| 42 and 109 | 4578 |