Least Common Multiple (LCM) of 37 and 169
The least common multiple (LCM) of 37 and 169 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 37 and 169?
First, calculate the GCD of 37 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 169 = 0 remainder 37 |
| 2 | 169 ÷ 37 = 4 remainder 21 |
| 3 | 37 ÷ 21 = 1 remainder 16 |
| 4 | 21 ÷ 16 = 1 remainder 5 |
| 5 | 16 ÷ 5 = 3 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 35 | 2065 |
| 91 and 106 | 9646 |
| 129 and 147 | 6321 |
| 116 and 86 | 4988 |
| 136 and 159 | 21624 |