Least Common Multiple (LCM) of 100 and 34
The least common multiple (LCM) of 100 and 34 is 1700.
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 100 and 34?
First, calculate the GCD of 100 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 34 = 2 remainder 32 |
| 2 | 34 ÷ 32 = 1 remainder 2 |
| 3 | 32 ÷ 2 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 63 | 12033 |
| 192 and 13 | 2496 |
| 154 and 131 | 20174 |
| 37 and 105 | 3885 |
| 191 and 162 | 30942 |