GCD goes by many different abbreviations:
Greatest Common Divisor
Highest Common Factor
Greatest Common Measure
Highest Common Divisor
LCM also goes by many different abbreviations:
Lowest Common Multiple
Least Common Multiple
Smallest Common Multiple
Lowest Common Denomination
GCD is the largest, positive whole number of each of the numbers you are comparing, can be divided by.
E.g 25 and 15 have a GCD of 5.
LCM is the smallest number that they both of the numbers you are comparing divide evenly into.
E.g 6 and 8 have a LCM of 24.
Method to work out the GCD:
Reduce your numbers to their constituent prime factors and identify the factors that are common in each.
E.g 72 and 90 72 = 2 x 2 x 2 x 3 x 3} 90 = 2 x 3 x 3 x 5} are the prime factors.
'2 x 3 x 3' is the common factor and 2 x 3 x 3 = 18.
Method to work out the LCM:
Using the prime factors used to find the GCD, multiply the common prime factors of both numbers together but only by the most number of times they appear in the numbers compared.
E.g 4 and 6 4 = 2 x 2} 6 = 2 x 3} are the prime factors.
Comparing '2 x 2' and '2 x 3', 2 is present more on the left side so we use that.
2² x 3 = 12.
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