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Secondary 1 | Maths

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Can someone explain to me how to get the last step pls

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