# LCM for 21 and 100

## What's the Least Common Multiple (LCM) of 21 and 100?

**Answer:**LCM of

**21 and 100**is

**2,100**

(Two thousand, one hundred)

## Finding LCM for 21 and 100 using GCF's of these numbers

The first method to find LCM for numbers 21 and 100 is to find Greatest Common Factor (GCF) of these numbers. Here's the formula:

LCM = (Number1 × Number2) ÷ GCF

GCF of numbers 21 and 100 is **1**, so

LCM = (21 × 100) ÷ 1

LCM = 2100 ÷ 1

LCM = 2100

## Finding LCM for 21 and 100 by Listing Multiples

The second method to find LCM for numbers 21 and 100 is to list out the common multiples for both nubmers and pick the first which matching:

**Multiples of 21**: 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 420, 441, 462, 483, 504, 525, 546, 567, 588, 609, 630, 651, 672, 693, 714, 735, 756, 777, 798, 819, 840, 861, 882, 903, 924, 945, 966, 987, 1008, 1029, 1050, 1071, 1092, 1113, 1134, 1155, 1176, 1197, 1218, 1239, 1260, 1281, 1302, 1323, 1344, 1365, 1386, 1407, 1428, 1449, 1470, 1491, 1512, 1533, 1554, 1575, 1596, 1617, 1638, 1659, 1680, 1701, 1722, 1743, 1764, 1785, 1806, 1827, 1848, 1869, 1890, 1911, 1932, 1953, 1974, 1995, 2016, 2037, 2058, 2079, **2100,** 2121, 2142

**Multiples of 100**: 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, **2100,** 2200, 2300

So the LCM for 21 and 100 is **2100**

## Finding LCM for 21 and 100 by Prime Factorization

Another method to find LCM for numbers 21 and 100 is to list all Prime Factors for both numbers and multiply the highest exponent prime factors:

All Prime Factors of 21: 3, 7 (exponent form: **3 ^{1}, 7^{1})**

All Prime Factors of 100: 2, 2, 5, 5 (exponent form: **2 ^{2}, 5^{2})**

3^{1} × 7^{1} × 2^{2} × 5^{2} = **2100**

## Related Calculations

## See Also

- Greatest Common Factor - Find the Greatest Common Factor (GCF) of two numbers

## LCM Table

## About "Least Common Multiple" Calculator

**2100**). Select the first number (e.g. '21') and the second number (e.g. '100'). After that hit the 'Calculate' button.

Least Common Multiple (LCM) also known as the Lowest Common Multiple or Smallest Common Multiple of 2 numbers - it is thesmallest positive integer that is divisible by both numbers