Least Common Multiple (LCM) of 32 and 61
The least common multiple (LCM) of 32 and 61 is 1952.
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 32 and 61?
First, calculate the GCD of 32 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 61 = 0 remainder 32 |
| 2 | 61 ÷ 32 = 1 remainder 29 |
| 3 | 32 ÷ 29 = 1 remainder 3 |
| 4 | 29 ÷ 3 = 9 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 145 | 23780 |
| 117 and 116 | 13572 |
| 109 and 78 | 8502 |
| 194 and 77 | 14938 |
| 99 and 35 | 3465 |