Question 6973: Can you tell me if these are correct. Find the greatest common divisor and least commmon multiple for the following numbers.
a. 45,36,24 GCD = 3 LCM= 12,960
b. 42,96,104,18 GCD = 2 LCM = 3,919,104
Thanks a ton.. They just dont seem right.
Answer by bonster(299)   (Show Source):
You can put this solution on YOUR website! a. 45,36,24
b. 42,96,104,18
In order to find the GCD, let's look at their prime factorization:
PROBLEM #1: GCD
45:  x  x 
36:  x x 
24:  x  x
Next, find the MINIMUM exponent of each base:
for 2, the minimum exponent is 0, written as
for 3, the minimum exponent is 1, written as
for 5 the minimum exponent is 0, written as
Multiply the minimum exponent of each base and you get:
x x = 3
******THE GCD FOR 45,36,24 = 3*****
PROBLEM #2: GCD
42:  x x  x 
96:  x x  x
104: x  x x 
18: x x x
Next, find the MINIMUM exponent of each base:
for 2, the minimum exponent is 1, written as
for 3, the minimum exponent is 0, written as
for 7 the minimum exponent is 0, written as
for 13 the minimum exponent is 0, written as
Multiply the minimum exponent of each base and you get:
x x x = 2
*****THE GCD FOR 42,96,104,18 = 2*****
PROBLEM #1: LCM
45: x x
36: x x
24: x x
Next, find the MAXIMUM exponent of each base:
for 2, the MAXIMUM exponent is 3, written as
for 3, theMAXIMUM exponent is 2, written as
for 5 the MAXIMUM exponent is 1, written as
Multiply the MAXIMUM exponent of each base and you get:
x x = 4x9x5=360
******THE LCM FOR 45,36,24 = 360*****
PROBLEM #2: LCM
42: x x x
96: x x x
104: x x x
18: x x x
Next, find the MAXIMUM exponent of each base:
for 2, the MAXIMUM exponent is 5, written as
for 3, the MAXIMUM exponent is 2, written as
for 7 the MAXIMUM exponent is 1, written as
for 13 the MAXIMUM exponent is 1, written as
Multiply the MAXIMUM exponent of each base and you get:
x x x = 26,208
*****THE LCM FOR 42,96,104,18 = 26,208*****
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