Least Common Multiple (LCM) of 21 and 60
The least common multiple (LCM) of 21 and 60 is 420.
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 21 and 60?
First, calculate the GCD of 21 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 60 = 0 remainder 21 |
| 2 | 60 ÷ 21 = 2 remainder 18 |
| 3 | 21 ÷ 18 = 1 remainder 3 |
| 4 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 20 | 640 |
| 170 and 95 | 3230 |
| 143 and 83 | 11869 |
| 20 and 124 | 620 |
| 126 and 52 | 3276 |