Elementary arithmetic, with brief notices of its history... by Robert Potts.

8

For 72 contains 18, 4 times, and 24, 3 times, and 3 and 4 being
primle to each other;
Wherefore the L.C.MI. of 18 and 24-1 sX24
6
'Or the least common multiple of two numbers, is equal to their product divided by their greatest common measure.
The following form is, perhaps, more convenient in practice.
L.C.M. of 18 and 24 = 18x42 = 18 x 24- 24x ls;
6 6 6
The least common multiple of two numbers is equal to the product of
either of the numbers multiplied by the quotient arising from dividing
the other by their greatest common measure.
If the two given numbers are prime to each other, their least
common multiple is equal to the product of the numbers.
To find the least cormmon multiple of more numbers than two:1. Of three numbers.
The L.C.M. of two of the numbers having been found, the
L.C.M. of this number and the third number will be the L.C.M. of
the three numbers.
2. Of four numbers.
The L.O.M. of three of the numbers having been found, the L.C..M.
of this number and the fourth number will be the L.C.M. of the four
numbers.
And so on for five, six, seven, &c., numbers.
When the several numbers are not large numbers, the process may
be shortened by successive divisions of the given numbers, by primo
factors which are common to two or more of the given numbers. By
this means, all the divisors will consist of the common prime factors,
and the numbers left after the divisions will be the factors which are
not common to any two of the numbers, Then the product of the
common prime factors, and the factors which are not common, will be
the least common multiple of all the given numbers.'
1 Exemplify by finding the least common multiple of 15, 24, 36, and 42 by both
methods.
Fiirst Method.
The G.C.M. of 24 and 36 is 12: the L.C.MI. 24 X3'72.,, G.C.. of 72 and 42 is 6: the L.C.M. =-2X2 504., G.C.I. of 504 and 15 is 3: the L.C.I. =- 15 =2520.
Second Mlethod.
2)15, 24, 36, 42
2)15, 12, 18, 21
3)15, 6, 9, 21
5, 2, 3, 7
Here 2, 2, 3 are the common prime factors, and 5, 2, 3, 7 are the factors not
Common.
L.C.M. of15, 24, 36, 42=2x2x3x5x2x3x7=2520.