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Marco and Elena trained for a swimming competition by swimming laps around a circular pool. They both started together at the same time from the pool’s edge. Marco completed each lap in 37 seconds, while Elena completed each lap in 55 seconds. How many laps had Marco completed the next time that Marco and Elena were together at the starting point?

Explanation	Calculations	Help
$We first factor each lap time into primes.$	$37 = 37 55 = 5 \times 11$	Theory & Tactics Method Card DIV4-C Click to view full details
$We then find the least common multiple of the two lap times by taking each prime with its highest exponent.$	$LCM = 37 \times 5 \times 11 = 2035$	Theory & Tactics Method Card DIV6-A Click to view full details
$We see that Marco's number of laps equals the total time until they meet divided by his lap time, so we write this division in factored form before simplifying.$	$\frac{2035}{37} = \frac{37 \times 5 \times 11}{37}$	Theory & Tactics Method Card FDPR2-A Click to view full details
$We cancel the common factor to obtain Marco's lap count.$	$\frac{37 \times 5 \times 11}{37} = \frac{37 \times 5 \times 11}{37} = 55$	Theory & Tactics Method Card FDPR2-A Click to view full details

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Marco and Elena trained for a swimming competition by swimming laps around a circular pool. They both started together at the same time from the pool’s edge. Marco completed each lap in 37 seconds, while Elena completed each lap in 55 seconds. How many laps had Marco completed the next time that Marco and Elena were together at the starting point?

Explanation	Calculations	Help
$We first factor each lap time into primes.$	$37 = 37 55 = 5 \times 11$	Theory & Tactics Method Card DIV4-C Click to view full details
$We then find the least common multiple of the two lap times by taking each prime with its highest exponent.$	$LCM = 37 \times 5 \times 11 = 2035$	Theory & Tactics Method Card DIV6-A Click to view full details
$We see that Marco's number of laps equals the total time until they meet divided by his lap time, so we write this division in factored form before simplifying.$	$\frac{2035}{37} = \frac{37 \times 5 \times 11}{37}$	Theory & Tactics Method Card FDPR2-A Click to view full details
$We cancel the common factor to obtain Marco's lap count.$	$\frac{37 \times 5 \times 11}{37} = \frac{37 \times 5 \times 11}{37} = 55$	Theory & Tactics Method Card FDPR2-A Click to view full details

Scroll horizontally to view all columns

D