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Secondary 1 | Maths
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Help Dylan! Anyone can contribute an answer, even non-tutors.
Can someone explain to me how to get the last step pls
Date Posted: 5 years ago
Views: 464
HCF = 68 = 2² x 17
LCM = 2040 = 2³ x 5 x 3 x 17
408 = 2³ x 3 x 17
Since the HCF is 2² x 17, X must contain 2² x 17 (if not it won't be the highest common factor)
Notice that the LCM contains a 5 that is not one of the prime factors of 408. This is telling you that the 5 comes from X.
(Recall that the LCM does contain factors that are found in one number but not the other)
The LCM contains a factor 3. 3 is in 408, but it is not found in X (if not the HCF would be 2² x 3 x 17 instead)
Similarly, the LCM contains 2³. It is in 408, but it is not found in X (if not the HCF would be 2³ x 17 instead)
X only contains 2².
So the smallest value of X is 2² x 5 x 17
= 340
Method 2 (shortcut)
For any 2 numbers A and B,
A x B = LCM x HCF
so X × 408 = 68 x 2040
X = 68 x 2040 ÷ 408
X = 340
LCM = 2040 = 2³ x 5 x 3 x 17
408 = 2³ x 3 x 17
Since the HCF is 2² x 17, X must contain 2² x 17 (if not it won't be the highest common factor)
Notice that the LCM contains a 5 that is not one of the prime factors of 408. This is telling you that the 5 comes from X.
(Recall that the LCM does contain factors that are found in one number but not the other)
The LCM contains a factor 3. 3 is in 408, but it is not found in X (if not the HCF would be 2² x 3 x 17 instead)
Similarly, the LCM contains 2³. It is in 408, but it is not found in X (if not the HCF would be 2³ x 17 instead)
X only contains 2².
So the smallest value of X is 2² x 5 x 17
= 340
Method 2 (shortcut)
For any 2 numbers A and B,
A x B = LCM x HCF
so X × 408 = 68 x 2040
X = 68 x 2040 ÷ 408
X = 340
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