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 Highest Common Factor (HCF), a.k.a. “Greatest Common Divisor (GCD) ” in America . Just as England
and the United States
are divided by a common language(*), 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
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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