Least Common Multiple (LCM) of 100 and 120
The least common multiple (LCM) of 100 and 120 is 600.
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 120?
First, calculate the GCD of 100 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 120 = 0 remainder 100 |
| 2 | 120 ÷ 100 = 1 remainder 20 |
| 3 | 100 ÷ 20 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 43 | 3139 |
| 31 and 189 | 5859 |
| 183 and 175 | 32025 |
| 137 and 180 | 24660 |
| 88 and 36 | 792 |