The LCM of three numbers is 7920 and their GCD is 12. Two of the numbers are 48 and 264. find the third number if one of its factors is 9.?
回答 (2)
2018-06-13 1:28 am
L.C.M. = 7920 = 2⁴ × 3² × 5 × 11
G.C.D. = 12 = 2² × 3
Both 9 (3²) and 12 (2² × 3) are factors of the third number. Hence, 2² and 3
Let the third number = 2² × 3² × y
48 = 2⁴ × 3
264 = 2³ × 3 × 11
By inspection, y = 5 or y = 5 × 11 = 55
The third number = 2² × 3² × 5 = 180
OR: The third number = 2² × 3² × 5 × 11 = 1980
G.C.D. = 12 = 2² × 3
Both 9 (3²) and 12 (2² × 3) are factors of the third number. Hence, 2² and 3
Let the third number = 2² × 3² × y
48 = 2⁴ × 3
264 = 2³ × 3 × 11
By inspection, y = 5 or y = 5 × 11 = 55
The third number = 2² × 3² × 5 = 180
OR: The third number = 2² × 3² × 5 × 11 = 1980
2018-06-13 10:36 am
The LCM of three numbers is 7920 and their GCD is 12.
Two of the numbers are 48 and 264.
Find the third number if one of its factors is 9.
LCM = 7920 = 2^4 × 3^2 × 5 × 11
GCD = 12 = 2^2 × 3
48 × 264 = 12672 = 2^7 × 3^2 × 11
2^2 × 3^2 × 5 × 11 = 1980
1980 is the third number.
Two of the numbers are 48 and 264.
Find the third number if one of its factors is 9.
LCM = 7920 = 2^4 × 3^2 × 5 × 11
GCD = 12 = 2^2 × 3
48 × 264 = 12672 = 2^7 × 3^2 × 11
2^2 × 3^2 × 5 × 11 = 1980
1980 is the third number.
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