15, 30, 45, . . .AS YOU CAN SEE, BOTH LISTS COULD HAVE STOPPED AT 30;...
15: 15, 30, 45, . . .As you can see, both lists could have stopped at 30; 30 is the LCM of 6 and 15. Sometimes it may be fasterto list out the multiples of the larger number first and see if the smaller number divides evenly into any ofthose multiples. In this case, we would have realized that 6 does not divide into 15 evenly, but it does divideinto 30 evenly; therefore, we found our LCM.Divisibility RulesTo aid in locating factors and multiples, some commonly known divisibility rules make finding them a littlequicker, especially without the use of a calculator.
3 2 6
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A R I T H M E T I C
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Divisibility by 2. If the number is even (the last digit, or units digit, is 0, 2, 4, 6, 8), the number isdivisible by 2.■
Divisibility by 3. If the sum of the digits adds to a multiple of 3, the entire number is divisible by 3.■
Divisibility by 4. If the last two digits of the number form a number that is divisible by 4, then theentire number is divisible by 4.■
Divisibility by 5. If the units digit is 0 or 5, the number is divisible by 5.■
Divisibility by 6. If the number is divisible by both 2 and 3, the entire number is divisible by 6.■
Divisibility by 9. If the sum of the digits adds to a multiple of 9, the entire number is divisible by 9.■
Divisibility by 10. If the units digit is 0, the number is divisible by 10.