Two positive integers have gcd (a, b) = 15 and lcm (a, b) = 90. Those two numbers are 15 and 90 or 30 and 45.
Suppose we have 2 positive integers, a and b, then:
gcd (a, b) = the greatest common divisor = common prime factors of a and b
lcm (a, b) = the least common multiple = multiplication of the greatest common prime factors of a and b
In the given problem:
gcd (a, b) = 15
prime factorization of 15:
15 = 3 x 5
Hence,
a = 3 x 5 x ....
b = 3 x 5 x ....
lcm (a, b) = 90
prime factorization of 90:
90 = 3 x 5 x 2 x 3
Therefore the possible pairs of a and b are:
Combination 1:
a = 3 x 5 = 15
b = 3 x 5 x 2 x 3 = 90
Combination 2:
a = 3 x 5 x 2 = 30
b = 3 x 5 x 3 = 35
We can conclude the two integers are 15 and 90 or 30 and 45.
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You would subtract 2/3 from 5/6 and that should give you 1/6
x=1/6
Answer:
1 and 1/2 days
Step-by-step explanation:
ITHINK ITS HELP GOOD LUCK
Answer:
x= 3, y=0, z= 1
Step-by-step explanation:
Let's label the 3 given equations first.
2x +3y +4z= 10 -----(1)
3x +2y -4z= 5 -----(2)
x +4y +2z= 5 -----(3)
(1) +(2):
<em>This</em><em> </em><em>is</em><em> </em><em>to</em><em> </em><em>eliminate</em><em> </em><em>the</em><em> </em><em>z</em><em> </em><em>term</em><em>.</em>
2x +3y +4z +3x +2y -4z= 10 +5
5x +5y= 15
<em>Divide</em><em> </em><em>by</em><em> </em><em>5</em><em> </em><em>on</em><em> </em><em>both</em><em> </em><em>sides</em><em>:</em>
x +y= 3 -----(4)
(3) ×2:
2x +8y +4z= 10 -----(5)
(2) +(5):
<em>This</em><em> </em><em>is</em><em> </em><em>to</em><em> </em><em>eliminate</em><em> </em><em>z</em><em> </em><em>term</em><em>.</em>
3x +2y -4z + 2x +8y +4z= 5 +10
5x +10y= 15
<em>Divide</em><em> </em><em>by</em><em> </em><em>5</em><em> </em><em>throughout</em><em>.</em>
x +2y= 3 -----(6)
(6) -(4):
x +2y -(x +y)= 3 -3
x +2y -x -y= 0
y= 0
subst. y=0 into (4):
x +0= 3
x= 3
subst. x=3, y=0 into (3):
3 +4(0) +2z= 5
3 +2z= 5
2z= 5 -3
2z= 2
z= 2÷2
z= 1
1600 bc if you use your calculator that’s what you get