Least Common Multiple (LCM) of 164 and 61
The least common multiple (LCM) of 164 and 61 is 10004.
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 164 and 61?
First, calculate the GCD of 164 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 61 = 2 remainder 42 |
| 2 | 61 ÷ 42 = 1 remainder 19 |
| 3 | 42 ÷ 19 = 2 remainder 4 |
| 4 | 19 ÷ 4 = 4 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 98 | 4214 |
| 85 and 154 | 13090 |
| 157 and 120 | 18840 |
| 122 and 174 | 10614 |
| 123 and 39 | 1599 |