4.d LCM + GCF

Question 1

What is the LCM?

Answer 1

The Lowest Common Multiple (LCM)

The smallest positive integer into which all the numbers of the set divide

Question 2

What is the LCM of 2 and 5?

Answer 2

10

As its the smallest number both 2 and 5 divide into

Question 3

What is the trick to calculate the LCM from two larger numbers?

Answer 3

1. Prime factorize both numbers
2. Of any repeated prime factors of the numbers, choose the one with the largest exponent. (if the same exponent, just select one)
3. Any non-repeated prime factors, select those too
4. Multiply all together!

Question 4

What is the LCM of 24 and 60?

Answer 4

24 = 2^3 x 3^1
60 = 2^2 x 3^1 x 5^1

so…
LCM = 2^3 x 3^1 x 5^1
= 120

Question 5

What is the LCM of 15, 18 and 24?

Answer 5

15 = 3 x 5
18 = 2 x 3^2
24 = 2^3 x 3

LCM = 2^3 x 3^2 x 5
= 360

Question 6

If two positive integers, x and y, share no prime factors, the LCM is _____

Answer 6

If two positive integers, x and y, share no prime factors, the LCM is xy

eg. 6 and 7
LCM = 6 * 7

Question 7

What is the GCF?

Answer 7

The Greatest Common Factor,

or the largest number that will divide into all numbers in a set

Question 8

What is the GCF of 8, 12 and 16?

Answer 8

4

Given that 4 is the largest number that divides into 8, 12 and 16.

Question 9

How do you find the GCF of two numbers?

Answer 9

1. Prime factorise each number
2. Identify repeated prime factors
3. Of any repeated prime factors, take only those with the SMALLEST exponent
4. Multiply only these numbers together

Question 10

What is no repeated prime factors are found? (GCF)

Answer 10

In that case the GCF is 1

Question 11

The GCF will always be LESS than or EQUAL to the ______________

Answer 11

The GCF will always be LESS than or EQUAL to the SMALLEST number in the set

Question 12

The LCM will always be GREATER than or EQUAL to the _____________

Answer 12

The LCM will always be GREATER than or EQUAL to the LARGEST number in the set

Question 13

If we know that the positive integer y divides evenly into x, what is the LCM and what is the GCF?

Answer 13

LCM = x
GCF = y

Question 14

How can you calculate the product of two numbers where you only know the LCM and the GCF?

Answer 14

x * y = GCF(x, y) * LCM(x, y)

Question 15

What do we need to find all the unique prime numbers in a set?

Answer 15

The LCM!

If you prime factorize the LCM, you will be able to see all unique prime factors that are also in the numbers in the set.

Question 16

If two or more entities return to a common starting point at various frequencies, then the shortest amount of time it takes for all the entities to return to the same starting point is the _________

Answer 16

If two or more entities return to a common starting point at various frequencies, then the shortest amount of time it takes for all the entities to return to the same starting point is the LCM !!!!