Least Common Multiple (LCM) of 100 and 138
The least common multiple (LCM) of 100 and 138 is 6900.
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 138?
First, calculate the GCD of 100 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 138 = 0 remainder 100 |
| 2 | 138 ÷ 100 = 1 remainder 38 |
| 3 | 100 ÷ 38 = 2 remainder 24 |
| 4 | 38 ÷ 24 = 1 remainder 14 |
| 5 | 24 ÷ 14 = 1 remainder 10 |
| 6 | 14 ÷ 10 = 1 remainder 4 |
| 7 | 10 ÷ 4 = 2 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 14 | 210 |
| 179 and 118 | 21122 |
| 69 and 129 | 2967 |
| 120 and 86 | 5160 |
| 91 and 175 | 2275 |