**How does it work?**

When we reduce a fraction to its lowest
terms, we actually cancel out as many common factors as possible. So eventually the numerator and the
denominator of original fraction get cancelled by their America . Just as England
and the United States
are divided by a common language

*Highest Common Factor*(HCF), a.k.a. “*Greatest Common Divisor*(GCD) ” in^{(*)}, we can divide 756 by 6 to get the HCF. Why? That is because 756 was divided by the HCF to get 6. You may try a similar trick with the denominators. You get the same conclusion.
It is useful to know that the product of

*two*numbers is equal to the product of their HCF and LCM. So 756 × 1386 = HCF × LCM. Hence we have
Observe that the bracketed
number (

^{756}/_{126}) is equal to 6 which is the numerator of the reduced fraction. So we do not even need to make that calculation. Just take the reduced numerator 6 and multiply that with the original denominator 1386 to get the LCM. You may try a similar trick with 1386 and 126. You end up multiplying 756 by 11, which gives the same answer.**Further Exploration**

Try the above with different pairs of
numbers. How can you extend this to find
the HCF and LCM of three or more numbers?

(*) OK, just kidding. In Singapore , we sort of follow
British English, but we are flexible.

**Suitable Levels*******Lower Secondary Mathematics (Sec 1 ~ grade 7)

* other syllabuses that involve factors,
HCF (GCD) and LCM

* any interested learner

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