What is a multiple in math?

The multiple of a number is the product of this number by any other number (0, 1, 2, 3, ...).

Our calculator works on the set of natural numbers, but there are multiples in the set of numbers, integers, real, etc. Therefore, a multiple can also be negative.

For example, the number 216 can be divided by 3 without a reminder. Like this, 216 is a multiple of 72, because, 3 times 72 equals 216. In other words, we can say that 216 is a multiple of 3 because there is a natural - 3 - which multiplied by 72 equals 216. The statement '216 is a multiple of 3' is equivalent '216 is divisible by 3', or that 3 is a divider of 216.

So to find the multiples of 72, simply multiply this number by a number of the set of natural numbers as many times as we want. See below how to do it for the number 72:

  • 72 x 0 = 0 so, 0 is a multiple of 72.
  • 72 x 1 = 72 so, 72 is a multiple of 72.
  • 72 x 2 = 144 so, 144 is a multiple of 72.
  • 72 x 3 = 216 so, 216 is a multiple of 72.
  • 72 x 4 = 288 so, 288 is a multiple of 72.
  • 72 x 5 = 360 so, 360 is a multiple of 72.
  • 72 x 6 = 432 so, 432 is a multiple of 72.
  • 72 x 7 = 504 so, 504 is a multiple of 72.
  • 72 x 8 = 576 so, 576 is a multiple of 72.
  • 72 x 9 = 648 so, 648 is a multiple of 72.
  • 72 x 10 = 720 so, 720 is a multiple of 72.
  • 72 x 11 = 792 so, 792 is a multiple of 72.
  • 72 x 12 = 864 so, 864 is a multiple of 72.
  • 72 x 13 = 936 so, 936 is a multiple of 72.
  • 72 x 14 = 1008 so, 1008 is a multiple of 72.
  • 72 x 15 = 1080 so, 1080 is a multiple of 72.
  • 72 x 16 = 1152 so, 1152 is a multiple of 72.
  • 72 x 17 = 1224 so, 1224 is a multiple of 72.
  • 72 x 18 = 1296 so, 1296 is a multiple of 72.
  • 72 x 19 = 1368 so, 1368 is a multiple of 72.

The first 20 multiples of 72 are: 0, 72, 144, 216, 288, 360, 432, 504, 576, 648, 720, 792, 864, 936, 1008, 1080, 1152, 1224, 1296, 1368.

Facts About Multiples

  • Any number is a multiple of itself (n x 1 = n).
  • Any number is a multiple of 1 (1 x n = n).
  • Zero is a multiple of any number (0 x n = 0).
  • The set of multiples of a number is an infinite set, since we can get this by multiplying the number given by all natural numbers.
    • The set of multiples of n can be represented by M n = {0 x n, 1 x n, 2 x n, 3 x n, 4 x n, ...} (where n is any natural). For example, the set of multiples of 72 is represented as M 72 = {0, 72,0,0,0, ...}.

Common Multiples

If two numbers are multiplied, then the product is a common multiple of these two numbers.

Example: if two numbers 72 and 3 are multiplied, then the result 216 is a common multiple of 72 and 3.

Note: The product of these two numbers is not necessarily the least common multiple-LCM of these numbers.

Multiples Table

  • 1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
  • 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40
  • 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60
  • 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80
  • 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100
  • 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120
  • 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140
  • 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160
  • 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180
  • 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200
  • 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220
  • 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240
  • 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195, 208, 221, 234, 247, 260
  • 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, 224, 238, 252, 266, 280
  • 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300

References:

  • Múltiplos e Divisores - atractor.pt

Multiples Examples

  • Multiples of 40
  • Multiples of 172
  • Multiples of 176
  • Multiples of 52
  • Multiples of 167
  • Multiples of 156
  • Multiples of 91
  • Multiples of 140
  • Multiples of 176

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