Finding Lowest Common Multiple

 In arithmetic and number theory, the lowest common multiple or (LCM) least common multiple or smallest common multiple of two rational numbers a and b is the smallest positive rational number that is an integer multiple of both a and b. (The definition may be extended to any two real numbers whose ratio is a rational number.) Since it is a multiple, it can be divided by a and b without a remainder. If either a or b is 0, so that there is no such positive integer, then LCM(a, b) is defined to be zero.- Source wikipedia

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Examples for finding lowest common multiple:

Example 1:

Find lowest common multiple for the number 24 and 34.
On finding the LCM we have to find the prime factors for the given number.
24      : 2 2 2 3
34      : 2          17
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LCM   : 2 2 2 3 17
Lowest common multiple for the numbers 24 and 34 is 2 * 2 * 2 * 3 * 17 = 408
Example 2:
Find lowest common multiple for the number 44 and 54.
On finding the LCM we have to find the prime factors for the given number.
44      : 2 2 11
54      : 2         3 3 3
----------------------------
LCM   : 2 2 11  3 3 3
Lowest common multiple for the numbers 44 and 54 is 2 * 2 * 11 * 3 * 3 * 3 = 1188
Example 3:
Find lowest common multiple for the number 64 and 84.
On finding the LCM we have to find the prime factors for the given number.
64      : 2 2 2 2 2 2
84      : 2 2            3 7
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LCM  :  2 2 2 2 2 2 3 7
Lowest common multiple for the numbers 64 and 84 is 2 * 2 * 2 * 2 * 2 * 2 * 3 * 7= 1344

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Practice problems for finding lowest common multiple:

Problem 1:
Find lowest common multiple for the number 242 and 342.
Lowest common multiple for the numbers 242  and 342 is 41382
Problem 2:
Find lowest common multiple for the number 224 and 324.
Lowest common multiple for the numbers 224 and 324is 18144
Problem 3:
Find lowest common multiple for the number 244 and 344.
Lowest common multiple for the numbers 244 and 344 is 20984