Drop the jaw noticeably. Keep the body of the tongue low and forward, and don't let the back of the tongue raise toward the soft palate. Pull the lip corners back slightly, almost a starting smile.

Americans pronounce algorithm as AL-guh-rih-dhuhm (/ˈælɡəˌrɪðəm/). The L in "algorithm" is a dark L — the back of the tongue rises toward the soft palate, adding a small "uh" quality before the L. This is called the Dark L vs Light L, the kind of sound shift that makes everyday speech feel effortless. It comes out as AL·guh·RIH·dhuhm. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "The algorithm was designed to personalize content recommendations".
Record yourself saying "algorithm" and play it back. The mic stays on your device — nothing's uploaded.
4 syllables, 9 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Drop the jaw noticeably. Keep the body of the tongue low and forward, and don't let the back of the tongue raise toward the soft palate. Pull the lip corners back slightly, almost a starting smile.

Keep the tongue tip down and pull the back of the tongue up toward the throat. The 'dark' sound comes from the back.

Curl or bunch your tongue without letting the tip touch the roof of your mouth. Brace the sides of your tongue against your upper back teeth, and round your lips slightly.
Drop your jaw slightly with relaxed lips. Touch the tongue tip behind the bottom front teeth and arch the top-front toward the roof.

Click any sentence to see the full breakdown — every link, every reduction, every flap-T.
The textbook way isn't wrong — it's just not how anyone actually says it.
The L in "algorithm" is a dark L — the back of the tongue rises toward the soft palate, adding a small "uh" quality before the L. Dark L adds a small schwa-like "uh" before the L. The back of the tongue lifts toward the soft palate.
Stress falls on the first syllable, not the others. Stretch AL — keep everything else short and quick.
Don't pronounce the first syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.