Least Common Multiple Problems - easy

Solution:
Since 6=3.2, then 6|3, so LCM(6;3)=6.

Solution:
Since 9=3.3, the LCM of 9 and 3 is 9.

Solution:
The first few multiples of 4 are 4,8,12,16,20,24,... and the first few multiples of 10 are 10,20,30,... The least number to appear in both sequences is 20, so it is the LCM of 4 and 10.

Solution:
Since 15=5.3, the LCM of 15 and 5 is 15.

Solution:
We see that 7 is a prime number and is therefore coprime with any number, which is not divisible by 7. 7 does not divide 12, so 7 and 12 are coprime numbers. Therefore their LCM is their product, 84.

Solution:
By factoring both numbers, we see that , and that . They have no common prime factors, so they are coprime. Therefore their least common multiple is their product, 72.

Solution:
Both 7 and 3 are prime, so they are also coprime. Then their LCM is their product, 21.

Solution:
By definition, LCM(12;9) is the smallest number, which divides both 12 and 9. If we factorize them, we see that and . So, if x is the LCM of 12 and 9, then x|3^2, x|3 and x|2^2. x|3 follows from x|3^2, so we are left with x|3^2 and x|2^2. Since 3^2 and 2^2 are coprime, x=2^2.3^2=4.9=36.