GMAT: GCF & LCM
How to find GCF/LCM using a Venn Diagram?
(1) Find prime factorization of two numbers (2) Create venn diagram and place each common factor, including copies of common factors appearing more than once, into the shared area of the diagram (3) Place the remaining (non-common) factors into the non-shared areas *The GCF is the product of primes in the overlapping region *The LCM is the product of all primes in the diagram
How to find GCF?
(1) Find prime factorizations (2) Find common prime factors (3) Multiply them together
How to find LCM?
(1) Find prime factorizations and GCF (2) Write each number in the form of GCF times another factor (3) Multiply these 3 factors
What is the range of the GCD?
1≤ GCD of set ≤ Smallest integer of set
GCF is also known as....
GCD (Greatest Common Denominator) HCF (Highest Common Factor)
How to keep LCM/GCF straight in your head?
GCF will always be smaller than or equal to the starting integers LCM will always be greater than or equal to the starting integers
What is the product of all integers in a set?
LCM * GCD
What is the range of the LCM?
Largest integer of set ≤ LCM of set
Every integer will have at least one common factor ...
One
What is the GCF for two numbers that have no primes in common?
One
How to find LCM? (Short-cut)
P*Q/GCF = LCM
What do we know about GCF?
That the factor of an integer can't be greater than the magnitude of the integer itself. Thus, the GCD of a set of integers can't be greater than the magnitude of the smallest integer of the set.
The Greatest Common Factor is equivalent to...
The Greatest Common DIVISOR
The Least Common Multiple is equivalent to...
The Least Common DENOMINATOR
The Greatest Common Factor is...
The largest factor/divisor of two or more integers
What do we know about LCM?
The multiple of an integer can't be smaller than the magnitude of the integer itself. Hence, the LCM of a set of integers can't be smaller than the magnitude of the largest integer of the set.
What is the LCM for two numbers that have no primes in common?
The product of those two numbers
The Least Common Multiple is...
The smallest multiple of two or more integers