Question

Mrs. Winston asks four students in her math class to find the least common multiple of 6 and 10. The students place their answers on the board. Which student answers the question correctly? *

Answer 1

Answer:

Step-by-step explanation:

The word "multiple" is in least common multiple.  A multiple of a number is a number you get by multiplying by another number.  Take the number 3 for example, since 3*2 = 6, then 6 is a multiple of 3.  3*3 = 9, so 9 is a multiple of 3.  3*4 = 12, so 12 is a multiple of 3, etc.

For our problem, if we want to find the LCM (least common multiple) of 6 and 10, start with the highest number and begin the multiplication process.  10*2 = 20.  So we know that 20 is a multiple of 10, but if 6 doesn't go into 20 evenly, then 20 is not a multiple of 6.  And 6 does not go into 20 evenly, so 20 isn't the LCM of 6 and 10.  

10*3 = 30, and 6 DOES go into 30 evenly (5 times) so 30 is the LCM of 6 and 10

Answer 2

Answer:30

Step-by-step explanation:

Find the prime factorization of 6

6 = 2 × 3

Find the prime factorization of 10

10 = 2 × 5

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 2 × 3 × 5

LCM = 30